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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 380880j
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 380880.j1 | 380880j1 | \([0, 0, 0, -220593, -178842733]\) | \(-687518464/7604375\) | \(-13130402902065270000\) | \([]\) | \(9123840\) | \(2.3505\) | \(\Gamma_0(N)\)-optimal |
| 380880.j2 | 380880j2 | \([0, 0, 0, 1969467, 4616512643]\) | \(489277573376/5615234375\) | \(-9695772464308593750000\) | \([]\) | \(27371520\) | \(2.8998\) |
Rank
sage: E.rank()
The elliptic curves in class 380880j have rank \(0\).
Complex multiplication
The elliptic curves in class 380880j do not have complex multiplication.Modular form 380880.2.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 Cremona numbering.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
