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SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 366912.r
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 366912.r1 | 366912r1 | \([0, 0, 0, -17052, -850640]\) | \(10536048/91\) | \(4736017907712\) | \([2]\) | \(1376256\) | \(1.2566\) | \(\Gamma_0(N)\)-optimal |
| 366912.r2 | 366912r2 | \([0, 0, 0, -5292, -2003120]\) | \(-78732/8281\) | \(-1723910518407168\) | \([2]\) | \(2752512\) | \(1.6031\) |
Rank
sage: E.rank()
The elliptic curves in class 366912.r have rank \(0\).
Complex multiplication
The elliptic curves in class 366912.r do not have complex multiplication.Modular form 366912.2.a.r
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.
