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SageMath
E = EllipticCurve("co1")
E.isogeny_class()
Elliptic curves in class 254100.co
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 254100.co1 | 254100co1 | \([0, 1, 0, -12285533, -11024152812]\) | \(463030539649024/149501953125\) | \(66212957395019531250000\) | \([2]\) | \(28224000\) | \(3.0824\) | \(\Gamma_0(N)\)-optimal |
| 254100.co2 | 254100co2 | \([0, 1, 0, 34980092, -75305402812]\) | \(667990736021936/732392128125\) | \(-5189909323573012500000000\) | \([2]\) | \(56448000\) | \(3.4289\) |
Rank
sage: E.rank()
The elliptic curves in class 254100.co have rank \(0\).
Complex multiplication
The elliptic curves in class 254100.co do not have complex multiplication.Modular form 254100.2.a.co
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.
