Properties

Label 350064.c
Number of curves $2$
Conductor $350064$
CM no
Rank $2$
Graph

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

Elliptic curves in class 350064.c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
350064.c1 350064c1 \([0, 0, 0, -13467, -428470]\) \(90458382169/25788048\) \(77002698719232\) \([2]\) \(1228800\) \(1.3712\) \(\Gamma_0(N)\)-optimal
350064.c2 350064c2 \([0, 0, 0, 35493, -2827510]\) \(1656015369191/2114999172\) \(-6315353687605248\) \([2]\) \(2457600\) \(1.7178\)  

Rank

sage: E.rank()
 

The elliptic curves in class 350064.c have rank \(2\).

Complex multiplication

The elliptic curves in class 350064.c do not have complex multiplication.

Modular form 350064.2.a.c

sage: E.q_eigenform(10)
 
\(q - 4 q^{5} + q^{11} - q^{13} - q^{17} - 2 q^{19} + O(q^{20})\)  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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.