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SageMath
E = EllipticCurve("db1")
E.isogeny_class()
Elliptic curves in class 94864.db
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
94864.db1 | 94864cs2 | \([0, -1, 0, -4887472, -3837475200]\) | \(15124197817/1294139\) | \(1104803965116409327616\) | \([2]\) | \(4423680\) | \(2.7790\) | |
94864.db2 | 94864cs1 | \([0, -1, 0, 330048, -277039552]\) | \(4657463/41503\) | \(-35431030951255109632\) | \([2]\) | \(2211840\) | \(2.4325\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 94864.db have rank \(0\).
Complex multiplication
The elliptic curves in class 94864.db do not have complex multiplication.Modular form 94864.2.a.db
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.