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SageMath
E = EllipticCurve("gf1")
E.isogeny_class()
Elliptic curves in class 78400gf
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 78400.eq1 | 78400gf1 | \([0, -1, 0, -99633, -12078863]\) | \(-177953104/125\) | \(-76832000000000\) | \([]\) | \(331776\) | \(1.6007\) | \(\Gamma_0(N)\)-optimal |
| 78400.eq2 | 78400gf2 | \([0, -1, 0, 96367, -51474863]\) | \(161017136/1953125\) | \(-1200500000000000000\) | \([]\) | \(995328\) | \(2.1500\) |
Rank
sage: E.rank()
The elliptic curves in class 78400gf have rank \(0\).
Complex multiplication
The elliptic curves in class 78400gf do not have complex multiplication.Modular form 78400.2.a.gf
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
