Properties

Label 158400.er
Number of curves $4$
Conductor $158400$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("er1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 158400.er

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
158400.er1 158400kt4 \([0, 0, 0, -224996700, 1299009526000]\) \(6749703004355978704/5671875\) \(1058508000000000000\) \([2]\) \(10616832\) \(3.1942\)  
158400.er2 158400kt3 \([0, 0, 0, -14059200, 20306401000]\) \(-26348629355659264/24169921875\) \(-281917968750000000000\) \([2]\) \(5308416\) \(2.8476\)  
158400.er3 158400kt2 \([0, 0, 0, -2840700, 1696894000]\) \(13584145739344/1195803675\) \(223165665043200000000\) \([2]\) \(3538944\) \(2.6448\)  
158400.er4 158400kt1 \([0, 0, 0, 196800, 123469000]\) \(72268906496/606436875\) \(-7073479710000000000\) \([2]\) \(1769472\) \(2.2983\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 158400.er have rank \(1\).

Complex multiplication

The elliptic curves in class 158400.er do not have complex multiplication.

Modular form 158400.2.a.er

sage: E.q_eigenform(10)
 
\(q - 2q^{7} + q^{11} + 2q^{13} - 2q^{19} + O(q^{20})\)  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.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.