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SageMath
E = EllipticCurve("bn1")
E.isogeny_class()
Elliptic curves in class 7056bn
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 7056.g2 | 7056bn1 | \([0, 0, 0, 3381, -92806]\) | \(596183/864\) | \(-6194316312576\) | \([]\) | \(11520\) | \(1.1401\) | \(\Gamma_0(N)\)-optimal |
| 7056.g1 | 7056bn2 | \([0, 0, 0, -102459, -12687766]\) | \(-16591834777/98304\) | \(-704775544897536\) | \([]\) | \(34560\) | \(1.6894\) |
Rank
sage: E.rank()
The elliptic curves in class 7056bn have rank \(1\).
Complex multiplication
The elliptic curves in class 7056bn do not have complex multiplication.Modular form 7056.2.a.bn
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
