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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 325822g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
325822.g2 | 325822g1 | \([1, 1, 0, -24670, -1495104]\) | \(647214625/3332\) | \(8549000394788\) | \([2]\) | \(794880\) | \(1.3273\) | \(\Gamma_0(N)\)-optimal |
325822.g1 | 325822g2 | \([1, 1, 0, -38360, 331142]\) | \(2433138625/1387778\) | \(3560658664429202\) | \([2]\) | \(1589760\) | \(1.6739\) |
Rank
sage: E.rank()
The elliptic curves in class 325822g have rank \(0\).
Complex multiplication
The elliptic curves in class 325822g do not have complex multiplication.Modular form 325822.2.a.g
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.