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SageMath
E = EllipticCurve("ee1")
E.isogeny_class()
Elliptic curves in class 117600.ee
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 117600.ee1 | 117600ig2 | \([0, 1, 0, -2368, 41768]\) | \(195112/9\) | \(67765824000\) | \([2]\) | \(138240\) | \(0.83977\) | |
| 117600.ee2 | 117600ig1 | \([0, 1, 0, 82, 2568]\) | \(64/3\) | \(-2823576000\) | \([2]\) | \(69120\) | \(0.49320\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 117600.ee have rank \(1\).
Complex multiplication
The elliptic curves in class 117600.ee do not have complex multiplication.Modular form 117600.2.a.ee
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.
