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SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 58080.r
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 58080.r1 | 58080k2 | \([0, -1, 0, -97795265, 372268086225]\) | \(14254800421166387776/269055826875\) | \(1952353524590599680000\) | \([2]\) | \(7372800\) | \(3.2093\) | |
| 58080.r2 | 58080k1 | \([0, -1, 0, -5910890, 6219113100]\) | \(-201440287521417664/30700866796875\) | \(-3480861330146475000000\) | \([2]\) | \(3686400\) | \(2.8627\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 58080.r have rank \(1\).
Complex multiplication
The elliptic curves in class 58080.r do not have complex multiplication.Modular form 58080.2.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.
