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Properties

Label 364650.c
Number of curves $2$
Conductor $364650$
CM no
Rank $2$
Graph

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Show commands: SageMath
E = EllipticCurve("c1")
 
E.isogeny_class()
 

Elliptic curves in class 364650.c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
364650.c1 364650c2 \([1, 1, 0, -3795, 64125]\) \(48375764105453/13074540336\) \(1634317542000\) \([2]\) \(868352\) \(1.0515\)  
364650.c2 364650c1 \([1, 1, 0, 605, 6925]\) \(195414916627/266982144\) \(-33372768000\) \([2]\) \(434176\) \(0.70497\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 364650.c have rank \(2\).

Complex multiplication

The elliptic curves in class 364650.c do not have complex multiplication.

Modular form 364650.2.a.c

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} + q^{6} - 4 q^{7} - q^{8} + q^{9} - q^{11} - q^{12} + q^{13} + 4 q^{14} + q^{16} + q^{17} - q^{18} - 4 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.