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SageMath
E = EllipticCurve("je1")
E.isogeny_class()
Elliptic curves in class 381150.je
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 381150.je1 | 381150je4 | \([1, -1, 1, -7247053265, 237455026687937]\) | \(260744057755293612689909/8504954620259328\) | \(1372984558732935073183104000\) | \([2]\) | \(368640000\) | \(4.3013\) | |
| 381150.je2 | 381150je3 | \([1, -1, 1, -472602065, 3370639923137]\) | \(72313087342699809269/11447096545640448\) | \(1847944815843148147851264000\) | \([2]\) | \(184320000\) | \(3.9547\) | |
| 381150.je3 | 381150je2 | \([1, -1, 1, -128233040, -553763948713]\) | \(1444540994277943589/15251205665388\) | \(2462055450684991744621500\) | \([2]\) | \(73728000\) | \(3.4965\) | |
| 381150.je4 | 381150je1 | \([1, -1, 1, -127906340, -556751293513]\) | \(1433528304665250149/162339408\) | \(26207018192302794000\) | \([2]\) | \(36864000\) | \(3.1500\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 381150.je have rank \(1\).
Complex multiplication
The elliptic curves in class 381150.je do not have complex multiplication.Modular form 381150.2.a.je
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 5 & 10 \\ 2 & 1 & 10 & 5 \\ 5 & 10 & 1 & 2 \\ 10 & 5 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
