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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 4002.f
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 4002.f1 | 4002f2 | \([1, 0, 1, -200195, 34459886]\) | \(887320005345582835753/5563780852176\) | \(5563780852176\) | \([2]\) | \(24576\) | \(1.6314\) | |
| 4002.f2 | 4002f1 | \([1, 0, 1, -12275, 559118]\) | \(-204520739414888233/17186581700352\) | \(-17186581700352\) | \([2]\) | \(12288\) | \(1.2848\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 4002.f have rank \(1\).
Complex multiplication
The elliptic curves in class 4002.f do not have complex multiplication.Modular form 4002.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
