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SageMath
E = EllipticCurve("x1")
E.isogeny_class()
Elliptic curves in class 20070x
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 20070.w1 | 20070x1 | \([1, -1, 1, -1228583, 525368927]\) | \(-7595793011867300157267/15324443312128000\) | \(-413759969427456000\) | \([3]\) | \(415584\) | \(2.2674\) | \(\Gamma_0(N)\)-optimal |
| 20070.w2 | 20070x2 | \([1, -1, 1, 2089177, 2594356831]\) | \(51234006909451962357/177433072000000000\) | \(-3492415156176000000000\) | \([]\) | \(1246752\) | \(2.8167\) |
Rank
sage: E.rank()
The elliptic curves in class 20070x have rank \(1\).
Complex multiplication
The elliptic curves in class 20070x do not have complex multiplication.Modular form 20070.2.a.x
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 Cremona 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 Cremona labels.
