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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 370881.j
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 370881.j1 | 370881j6 | \([1, -1, 1, -290778431, -1908423925180]\) | \(53297461115137/147\) | \(7499306271608652627\) | \([2]\) | \(38535168\) | \(3.2801\) | |
| 370881.j2 | 370881j4 | \([1, -1, 1, -18180896, -29790752974]\) | \(13027640977/21609\) | \(1102398021926471936169\) | \([2, 2]\) | \(19267584\) | \(2.9335\) | |
| 370881.j3 | 370881j3 | \([1, -1, 1, -14472086, 21065933270]\) | \(6570725617/45927\) | \(2342997545144017613607\) | \([2]\) | \(19267584\) | \(2.9335\) | |
| 370881.j4 | 370881j5 | \([1, -1, 1, -12617681, -48369665788]\) | \(-4354703137/17294403\) | \(-882285883548486372913923\) | \([2]\) | \(38535168\) | \(3.2801\) | |
| 370881.j5 | 370881j2 | \([1, -1, 1, -1491251, -149943454]\) | \(7189057/3969\) | \(202481269333433620929\) | \([2, 2]\) | \(9633792\) | \(2.5870\) | |
| 370881.j6 | 370881j1 | \([1, -1, 1, 363154, -18651580]\) | \(103823/63\) | \(-3213988402117993983\) | \([2]\) | \(4816896\) | \(2.2404\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 370881.j have rank \(1\).
Complex multiplication
The elliptic curves in class 370881.j do not have complex multiplication.Modular form 370881.2.a.j
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.
\(\left(\begin{array}{rrrrrr} 1 & 2 & 8 & 4 & 4 & 8 \\ 2 & 1 & 4 & 2 & 2 & 4 \\ 8 & 4 & 1 & 8 & 2 & 4 \\ 4 & 2 & 8 & 1 & 4 & 8 \\ 4 & 2 & 2 & 4 & 1 & 2 \\ 8 & 4 & 4 & 8 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
