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SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 15680.r
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 15680.r1 | 15680v2 | \([0, 1, 0, -3735041, -2779534241]\) | \(544737993463/20000\) | \(211569119068160000\) | \([2]\) | \(430080\) | \(2.4121\) | |
| 15680.r2 | 15680v1 | \([0, 1, 0, -222721, -47651745]\) | \(-115501303/25600\) | \(-270808472407244800\) | \([2]\) | \(215040\) | \(2.0655\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 15680.r have rank \(0\).
Complex multiplication
The elliptic curves in class 15680.r do not have complex multiplication.Modular form 15680.2.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.
