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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 63480.j
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 63480.j1 | 63480l4 | \([0, -1, 0, -558800, -158032500]\) | \(63649751618/1164375\) | \(353012302344960000\) | \([2]\) | \(811008\) | \(2.1620\) | |
| 63480.j2 | 63480l2 | \([0, -1, 0, -72120, 3739932]\) | \(273671716/119025\) | \(18042851008742400\) | \([2, 2]\) | \(405504\) | \(1.8154\) | |
| 63480.j3 | 63480l1 | \([0, -1, 0, -61540, 5894020]\) | \(680136784/345\) | \(13074529716480\) | \([4]\) | \(202752\) | \(1.4688\) | \(\Gamma_0(N)\)-optimal |
| 63480.j4 | 63480l3 | \([0, -1, 0, 245280, 27481452]\) | \(5382838942/4197615\) | \(-1272622424483297280\) | \([2]\) | \(811008\) | \(2.1620\) |
Rank
sage: E.rank()
The elliptic curves in class 63480.j have rank \(0\).
Complex multiplication
The elliptic curves in class 63480.j do not have complex multiplication.Modular form 63480.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
