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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 2760.h
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 2760.h1 | 2760h3 | \([0, 1, 0, -2160176, -1222750176]\) | \(544328872410114151778/14166950625\) | \(29013914880000\) | \([2]\) | \(24576\) | \(2.0986\) | |
| 2760.h2 | 2760h4 | \([0, 1, 0, -209696, 4219680]\) | \(497927680189263938/284271240234375\) | \(582187500000000000\) | \([2]\) | \(24576\) | \(2.0986\) | |
| 2760.h3 | 2760h2 | \([0, 1, 0, -135176, -19090176]\) | \(266763091319403556/1355769140625\) | \(1388307600000000\) | \([2, 2]\) | \(12288\) | \(1.7520\) | |
| 2760.h4 | 2760h1 | \([0, 1, 0, -3956, -614400]\) | \(-26752376766544/618796614375\) | \(-158411933280000\) | \([4]\) | \(6144\) | \(1.4054\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 2760.h have rank \(1\).
Complex multiplication
The elliptic curves in class 2760.h do not have complex multiplication.Modular form 2760.2.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.
