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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 369600.h
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 369600.h1 | 369600h3 | \([0, -1, 0, -15260033, 22914971937]\) | \(95946737295893401/168104301750\) | \(688555219968000000000\) | \([2]\) | \(28311552\) | \(2.8918\) | |
| 369600.h2 | 369600h4 | \([0, -1, 0, -12348033, -16600644063]\) | \(50834334659676121/338378906250\) | \(1386000000000000000000\) | \([2]\) | \(28311552\) | \(2.8918\) | |
| 369600.h3 | 369600h2 | \([0, -1, 0, -1260033, 108971937]\) | \(54014438633401/30015562500\) | \(122943744000000000000\) | \([2, 2]\) | \(14155776\) | \(2.5452\) | |
| 369600.h4 | 369600h1 | \([0, -1, 0, 307967, 13323937]\) | \(788632918919/475398000\) | \(-1947230208000000000\) | \([2]\) | \(7077888\) | \(2.1987\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 369600.h have rank \(0\).
Complex multiplication
The elliptic curves in class 369600.h do not have complex multiplication.Modular form 369600.2.a.h
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.
