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SageMath
E = EllipticCurve("bj1")
E.isogeny_class()
Elliptic curves in class 7488bj
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 7488.k2 | 7488bj1 | \([0, 0, 0, 324, 2160]\) | \(11664/13\) | \(-4192321536\) | \([2]\) | \(3072\) | \(0.53286\) | \(\Gamma_0(N)\)-optimal |
| 7488.k1 | 7488bj2 | \([0, 0, 0, -1836, 20304]\) | \(530604/169\) | \(218000719872\) | \([2]\) | \(6144\) | \(0.87944\) |
Rank
sage: E.rank()
The elliptic curves in class 7488bj have rank \(1\).
Complex multiplication
The elliptic curves in class 7488bj do not have complex multiplication.Modular form 7488.2.a.bj
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.
