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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 90354g
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 90354.i2 | 90354g1 | \([1, 0, 1, 6368559, -13696226156]\) | \(8132677436375/27779483952\) | \(-97574866621928142975792\) | \([3]\) | \(7032960\) | \(3.0943\) | \(\Gamma_0(N)\)-optimal |
| 90354.i1 | 90354g2 | \([1, 0, 1, -301348416, -2017081437554]\) | \(-861621756231273625/1763284267008\) | \(-6193499759287750596538368\) | \([]\) | \(21098880\) | \(3.6436\) |
Rank
sage: E.rank()
The elliptic curves in class 90354g have rank \(0\).
Complex multiplication
The elliptic curves in class 90354g do not have complex multiplication.Modular form 90354.2.a.g
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.
