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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 235340g
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 235340.g1 | 235340g1 | \([0, 0, 0, -87412, -3514971]\) | \(971882496/492205\) | \(37408400927062480\) | \([2]\) | \(1128960\) | \(1.8726\) | \(\Gamma_0(N)\)-optimal |
| 235340.g2 | 235340g2 | \([0, 0, 0, 324433, -27154874]\) | \(3105672624/2059225\) | \(-2504072551852345600\) | \([2]\) | \(2257920\) | \(2.2192\) |
Rank
sage: E.rank()
The elliptic curves in class 235340g have rank \(1\).
Complex multiplication
The elliptic curves in class 235340g do not have complex multiplication.Modular form 235340.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
