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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 116886.g
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 116886.g1 | 116886f4 | \([1, 1, 0, -1159889304, -15204991845600]\) | \(97413070452067229637409633/140666577176907936\) | \(249199422130100200008096\) | \([2]\) | \(44236800\) | \(3.7601\) | |
| 116886.g2 | 116886f3 | \([1, 1, 0, -185810264, 657634198368]\) | \(400476194988122984445793/126270124548858769248\) | \(223695228115900790107756128\) | \([2]\) | \(44236800\) | \(3.7601\) | |
| 116886.g3 | 116886f2 | \([1, 1, 0, -73154424, -233045403840]\) | \(24439335640029940889953/902916953746891776\) | \(1599572461496797341582336\) | \([2, 2]\) | \(22118400\) | \(3.4135\) | |
| 116886.g4 | 116886f1 | \([1, 1, 0, 1807496, -13002183872]\) | \(368637286278891167/41443067603976192\) | \(-73418922287567666675712\) | \([2]\) | \(11059200\) | \(3.0669\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 116886.g have rank \(1\).
Complex multiplication
The elliptic curves in class 116886.g do not have complex multiplication.Modular form 116886.2.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 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.
