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SageMath
E = EllipticCurve("dc1")
E.isogeny_class()
Elliptic curves in class 35280.dc
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 35280.dc1 | 35280fw2 | \([0, 0, 0, -661647, 131060986]\) | \(4253563312/1476225\) | \(11117378955984940800\) | \([2]\) | \(860160\) | \(2.3562\) | |
| 35280.dc2 | 35280fw1 | \([0, 0, 0, -275772, -54236189]\) | \(4927700992/151875\) | \(71485204192290000\) | \([2]\) | \(430080\) | \(2.0096\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 35280.dc have rank \(1\).
Complex multiplication
The elliptic curves in class 35280.dc do not have complex multiplication.Modular form 35280.2.a.dc
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.
