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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 76664.j
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 76664.j1 | 76664i2 | \([0, -1, 0, -2004672, -1067303380]\) | \(169556172914/4353013\) | \(22873375565456009216\) | \([2]\) | \(2363904\) | \(2.4969\) | |
| 76664.j2 | 76664i1 | \([0, -1, 0, 21448, -53432932]\) | \(415292/469567\) | \(-1233695183559580672\) | \([2]\) | \(1181952\) | \(2.1504\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 76664.j have rank \(0\).
Complex multiplication
The elliptic curves in class 76664.j do not have complex multiplication.Modular form 76664.2.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.
