Properties

Label 141120.md
Number of curves $8$
Conductor $141120$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("md1")
 
E.isogeny_class()
 

Elliptic curves in class 141120.md

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
141120.md1 141120bd8 \([0, 0, 0, -182073612, -594925855216]\) \(29689921233686449/10380965400750\) \(233396013539665639047168000\) \([2]\) \(42467328\) \(3.7610\)  
141120.md2 141120bd5 \([0, 0, 0, -162599052, -798040774384]\) \(21145699168383889/2593080\) \(58300409588660305920\) \([2]\) \(14155776\) \(3.2117\)  
141120.md3 141120bd6 \([0, 0, 0, -76233612, 249380992784]\) \(2179252305146449/66177562500\) \(1487875036377268224000000\) \([2, 2]\) \(21233664\) \(3.4144\)  
141120.md4 141120bd3 \([0, 0, 0, -75669132, 253352899856]\) \(2131200347946769/2058000\) \(46270166340206592000\) \([2]\) \(10616832\) \(3.0679\)  
141120.md5 141120bd2 \([0, 0, 0, -10189452, -12399768304]\) \(5203798902289/57153600\) \(1284988619505165926400\) \([2, 2]\) \(7077888\) \(2.8651\)  
141120.md6 141120bd4 \([0, 0, 0, -2286732, -31141859056]\) \(-58818484369/18600435000\) \(-418194956972886589440000\) \([2]\) \(14155776\) \(3.2117\)  
141120.md7 141120bd1 \([0, 0, 0, -1157772, 168717584]\) \(7633736209/3870720\) \(87025684283947745280\) \([2]\) \(3538944\) \(2.5186\) \(\Gamma_0(N)\)-optimal
141120.md8 141120bd7 \([0, 0, 0, 20574708, 839485788176]\) \(42841933504271/13565917968750\) \(-305003537887104000000000000\) \([2]\) \(42467328\) \(3.7610\)  

Rank

sage: E.rank()
 

The elliptic curves in class 141120.md have rank \(1\).

Complex multiplication

The elliptic curves in class 141120.md do not have complex multiplication.

Modular form 141120.2.a.md

sage: E.q_eigenform(10)
 
\(q + q^{5} + 2 q^{13} - 6 q^{17} + 4 q^{19} + O(q^{20})\) Copy content Toggle raw display

Isogeny matrix

sage: E.isogeny_class().matrix()
 

The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the LMFDB numbering.

\(\left(\begin{array}{rrrrrrrr} 1 & 3 & 2 & 4 & 6 & 12 & 12 & 4 \\ 3 & 1 & 6 & 12 & 2 & 4 & 4 & 12 \\ 2 & 6 & 1 & 2 & 3 & 6 & 6 & 2 \\ 4 & 12 & 2 & 1 & 6 & 12 & 3 & 4 \\ 6 & 2 & 3 & 6 & 1 & 2 & 2 & 6 \\ 12 & 4 & 6 & 12 & 2 & 1 & 4 & 3 \\ 12 & 4 & 6 & 3 & 2 & 4 & 1 & 12 \\ 4 & 12 & 2 & 4 & 6 & 3 & 12 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with LMFDB labels.