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SageMath
E = EllipticCurve("gf1")
E.isogeny_class()
Elliptic curves in class 145200.gf
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 145200.gf1 | 145200ho3 | \([0, 1, 0, -2130608, 1196314788]\) | \(37736227588/33\) | \(935384208000000\) | \([2]\) | \(2949120\) | \(2.1730\) | |
| 145200.gf2 | 145200ho4 | \([0, 1, 0, -315608, -42241212]\) | \(122657188/43923\) | \(1244996380848000000\) | \([2]\) | \(2949120\) | \(2.1730\) | |
| 145200.gf3 | 145200ho2 | \([0, 1, 0, -134108, 18379788]\) | \(37642192/1089\) | \(7716919716000000\) | \([2, 2]\) | \(1474560\) | \(1.8264\) | |
| 145200.gf4 | 145200ho1 | \([0, 1, 0, 2017, 955788]\) | \(2048/891\) | \(-394615212750000\) | \([2]\) | \(737280\) | \(1.4798\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 145200.gf have rank \(1\).
Complex multiplication
The elliptic curves in class 145200.gf do not have complex multiplication.Modular form 145200.2.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 LMFDB numbering.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
