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SageMath
E = EllipticCurve("bg1")
E.isogeny_class()
Elliptic curves in class 103056.bg
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 103056.bg1 | 103056bd1 | \([0, 1, 0, -7918136, 5056370772]\) | \(13403946614821979039929/5057590268826067968\) | \(20715889741111574396928\) | \([2]\) | \(15175680\) | \(2.9817\) | \(\Gamma_0(N)\)-optimal |
| 103056.bg2 | 103056bd2 | \([0, 1, 0, 24770504, 36110578772]\) | \(410363075617640914325831/374944243169850027552\) | \(-1535771620023705712852992\) | \([2]\) | \(30351360\) | \(3.3282\) |
Rank
sage: E.rank()
The elliptic curves in class 103056.bg have rank \(0\).
Complex multiplication
The elliptic curves in class 103056.bg do not have complex multiplication.Modular form 103056.2.a.bg
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 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.
