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SageMath
E = EllipticCurve("ei1")
E.isogeny_class()
Elliptic curves in class 286650.ei
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
286650.ei1 | 286650ei2 | \([1, -1, 0, -1483092, -694922544]\) | \(-168256703745625/30371328\) | \(-65120774804467200\) | \([]\) | \(4478976\) | \(2.2300\) | |
286650.ei2 | 286650ei1 | \([1, -1, 0, 5283, -3185379]\) | \(7604375/2047032\) | \(-4389149855071800\) | \([]\) | \(1492992\) | \(1.6807\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 286650.ei have rank \(0\).
Complex multiplication
The elliptic curves in class 286650.ei do not have complex multiplication.Modular form 286650.2.a.ei
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.