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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 62790.o
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 62790.o1 | 62790n4 | \([1, 0, 1, -15844634, -24277000804]\) | \(439916557267933889175323929/4458152790000\) | \(4458152790000\) | \([2]\) | \(2457600\) | \(2.4571\) | |
| 62790.o2 | 62790n3 | \([1, 0, 1, -1065914, -318104548]\) | \(133933625659475879649049/33817997565232891920\) | \(33817997565232891920\) | \([2]\) | \(2457600\) | \(2.4571\) | |
| 62790.o3 | 62790n2 | \([1, 0, 1, -990314, -379370788]\) | \(107409288013422469722649/10811890310457600\) | \(10811890310457600\) | \([2, 2]\) | \(1228800\) | \(2.1105\) | |
| 62790.o4 | 62790n1 | \([1, 0, 1, -57194, -6869284]\) | \(-20690177179494572569/8383049989816320\) | \(-8383049989816320\) | \([2]\) | \(614400\) | \(1.7640\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 62790.o have rank \(1\).
Complex multiplication
The elliptic curves in class 62790.o do not have complex multiplication.Modular form 62790.2.a.o
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
