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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 337896.j
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 337896.j1 | 337896j2 | \([0, 0, 0, -18411, -644746]\) | \(530604/169\) | \(219822443523072\) | \([2]\) | \(912384\) | \(1.4558\) | |
| 337896.j2 | 337896j1 | \([0, 0, 0, 3249, -68590]\) | \(11664/13\) | \(-4227354683136\) | \([2]\) | \(456192\) | \(1.1092\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 337896.j have rank \(0\).
Complex multiplication
The elliptic curves in class 337896.j do not have complex multiplication.Modular form 337896.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
