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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 233289.f
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 233289.f1 | 233289f2 | \([0, 0, 1, -4343619, 3487180828]\) | \(-1713910976512/1594323\) | \(-8430764066371668987\) | \([]\) | \(7907328\) | \(2.5544\) | |
| 233289.f2 | 233289f1 | \([0, 0, 1, -11109, -489722]\) | \(-28672/3\) | \(-15863969972907\) | \([]\) | \(608256\) | \(1.2720\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 233289.f have rank \(2\).
Complex multiplication
The elliptic curves in class 233289.f do not have complex multiplication.Modular form 233289.2.a.f
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.
\(\left(\begin{array}{rr} 1 & 13 \\ 13 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
