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SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 79560.r
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 79560.r1 | 79560i2 | \([0, 0, 0, -388623, 93244322]\) | \(34780972302198736/1711783125\) | \(319459813920000\) | \([2]\) | \(491520\) | \(1.8550\) | |
| 79560.r2 | 79560i1 | \([0, 0, 0, -22998, 1618697]\) | \(-115331093579776/30301171875\) | \(-353432868750000\) | \([2]\) | \(245760\) | \(1.5084\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 79560.r have rank \(1\).
Complex multiplication
The elliptic curves in class 79560.r do not have complex multiplication.Modular form 79560.2.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.
