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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 15210.g
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 15210.g1 | 15210h3 | \([1, -1, 0, -735435, 242893795]\) | \(12501706118329/2570490\) | \(9044895650212890\) | \([2]\) | \(172032\) | \(2.0588\) | |
| 15210.g2 | 15210h2 | \([1, -1, 0, -50985, 2925625]\) | \(4165509529/1368900\) | \(4816808334432900\) | \([2, 2]\) | \(86016\) | \(1.7122\) | |
| 15210.g3 | 15210h1 | \([1, -1, 0, -20565, -1095899]\) | \(273359449/9360\) | \(32935441602960\) | \([2]\) | \(43008\) | \(1.3657\) | \(\Gamma_0(N)\)-optimal |
| 15210.g4 | 15210h4 | \([1, -1, 0, 146745, 19969951]\) | \(99317171591/106616250\) | \(-375155264508716250\) | \([2]\) | \(172032\) | \(2.0588\) |
Rank
sage: E.rank()
The elliptic curves in class 15210.g have rank \(0\).
Complex multiplication
The elliptic curves in class 15210.g do not have complex multiplication.Modular form 15210.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
