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SageMath
E = EllipticCurve("bv1")
E.isogeny_class()
Elliptic curves in class 322050bv
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 322050bv have rank \(0\).
Complex multiplication
The elliptic curves in class 322050bv do not have complex multiplication.Modular form 322050.2.a.bv
sage: E.q_eigenform(10)
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.