Properties

Label 331200jf
Number of curves $6$
Conductor $331200$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("jf1")
 
E.isogeny_class()
 

Elliptic curves in class 331200jf

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
331200.jf5 331200jf1 \([0, 0, 0, -6048300, -6281282000]\) \(-8194759433281/965779200\) \(-2883801238732800000000\) \([2]\) \(14155776\) \(2.8536\) \(\Gamma_0(N)\)-optimal
331200.jf4 331200jf2 \([0, 0, 0, -99360300, -381208898000]\) \(36330796409313601/428490000\) \(1279464284160000000000\) \([2, 2]\) \(28311552\) \(3.2002\)  
331200.jf3 331200jf3 \([0, 0, 0, -101952300, -360270722000]\) \(39248884582600321/3935264062500\) \(11750635526400000000000000\) \([2, 2]\) \(56623104\) \(3.5468\)  
331200.jf1 331200jf4 \([0, 0, 0, -1589760300, -24397514498000]\) \(148809678420065817601/20700\) \(61809868800000000\) \([2]\) \(56623104\) \(3.5468\)  
331200.jf2 331200jf5 \([0, 0, 0, -371952300, 2365109278000]\) \(1905890658841300321/293666194803750\) \(876882559024880640000000000\) \([2]\) \(113246208\) \(3.8933\)  
331200.jf6 331200jf6 \([0, 0, 0, 126575700, -1745607458000]\) \(75108181893694559/484313964843750\) \(-1446153750000000000000000000\) \([2]\) \(113246208\) \(3.8933\)  

Rank

sage: E.rank()
 

The elliptic curves in class 331200jf have rank \(0\).

Complex multiplication

The elliptic curves in class 331200jf do not have complex multiplication.

Modular form 331200.2.a.jf

sage: E.q_eigenform(10)
 
\(q + 4 q^{11} - 2 q^{13} - 6 q^{17} - 4 q^{19} + O(q^{20})\) 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 Cremona numbering.

\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 2 & 2 \\ 4 & 2 & 4 & 1 & 8 & 8 \\ 8 & 4 & 2 & 8 & 1 & 4 \\ 8 & 4 & 2 & 8 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.