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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 31680l
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
31680.m2 | 31680l1 | \([0, 0, 0, 1077, 4372]\) | \(2961169856/1890625\) | \(-88209000000\) | \([2]\) | \(18432\) | \(0.78922\) | \(\Gamma_0(N)\)-optimal |
31680.m1 | 31680l2 | \([0, 0, 0, -4548, 35872]\) | \(3484156096/1830125\) | \(5464723968000\) | \([2]\) | \(36864\) | \(1.1358\) |
Rank
sage: E.rank()
The elliptic curves in class 31680l have rank \(0\).
Complex multiplication
The elliptic curves in class 31680l do not have complex multiplication.Modular form 31680.2.a.l
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.