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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 35574g
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 35574.l2 | 35574g1 | \([1, 1, 0, -438869, 369685485]\) | \(-33698267/193536\) | \(-53688858125116161024\) | \([2]\) | \(1520640\) | \(2.4697\) | \(\Gamma_0(N)\)-optimal |
| 35574.l1 | 35574g2 | \([1, 1, 0, -10873909, 13770363853]\) | \(512576216027/1143072\) | \(317099818301467326048\) | \([2]\) | \(3041280\) | \(2.8163\) |
Rank
sage: E.rank()
The elliptic curves in class 35574g have rank \(0\).
Complex multiplication
The elliptic curves in class 35574g do not have complex multiplication.Modular form 35574.2.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.
