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SageMath
E = EllipticCurve("ig1")
E.isogeny_class()
Elliptic curves in class 62400ig
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
62400.ib2 | 62400ig1 | \([0, 1, 0, -793, -8857]\) | \(107850176/117\) | \(59904000\) | \([2]\) | \(28672\) | \(0.40795\) | \(\Gamma_0(N)\)-optimal |
62400.ib1 | 62400ig2 | \([0, 1, 0, -993, -4257]\) | \(26463592/13689\) | \(56070144000\) | \([2]\) | \(57344\) | \(0.75452\) |
Rank
sage: E.rank()
The elliptic curves in class 62400ig have rank \(1\).
Complex multiplication
The elliptic curves in class 62400ig do not have complex multiplication.Modular form 62400.2.a.ig
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.