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SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 70980r
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 70980.t1 | 70980r1 | \([0, 1, 0, -901, 3524]\) | \(1048576/525\) | \(40545195600\) | \([2]\) | \(51840\) | \(0.72826\) | \(\Gamma_0(N)\)-optimal |
| 70980.t2 | 70980r2 | \([0, 1, 0, 3324, 30564]\) | \(3286064/2205\) | \(-2724637144320\) | \([2]\) | \(103680\) | \(1.0748\) |
Rank
sage: E.rank()
The elliptic curves in class 70980r have rank \(0\).
Complex multiplication
The elliptic curves in class 70980r do not have complex multiplication.Modular form 70980.2.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 Cremona 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 Cremona labels.
