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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 3420.f
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 3420.f1 | 3420a1 | \([0, 0, 0, -8292, -271051]\) | \(5405726654464/407253125\) | \(4750200450000\) | \([2]\) | \(5760\) | \(1.1777\) | \(\Gamma_0(N)\)-optimal |
| 3420.f2 | 3420a2 | \([0, 0, 0, 7953, -1203514]\) | \(298091207216/3525390625\) | \(-657922500000000\) | \([2]\) | \(11520\) | \(1.5243\) |
Rank
sage: E.rank()
The elliptic curves in class 3420.f have rank \(0\).
Complex multiplication
The elliptic curves in class 3420.f do not have complex multiplication.Modular form 3420.2.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.
