Properties

Label 322050.bv
Number of curves $2$
Conductor $322050$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("bv1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 322050.bv

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
322050.bv1 322050bv1 \([1, 0, 0, -12372088, -9881910208]\) \(13403946614821979039929/5057590268826067968\) \(79024847950407312000000\) \([2]\) \(50585600\) \(3.0932\) \(\Gamma_0(N)\)-optimal
322050.bv2 322050bv2 \([1, 0, 0, 38703912, -70509122208]\) \(410363075617640914325831/374944243169850027552\) \(-5858503799528906680500000\) \([2]\) \(101171200\) \(3.4398\)  

Rank

sage: E.rank()
 

The elliptic curves in class 322050.bv have rank \(0\).

Complex multiplication

The elliptic curves in class 322050.bv do not have complex multiplication.

Modular form 322050.2.a.bv

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