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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 8190.f
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 8190.f1 | 8190j2 | \([1, -1, 0, -50625, 4102461]\) | \(19683218700810001/1478750000000\) | \(1078008750000000\) | \([2]\) | \(53760\) | \(1.6298\) | |
| 8190.f2 | 8190j1 | \([1, -1, 0, -10305, -324675]\) | \(166021325905681/32614400000\) | \(23775897600000\) | \([2]\) | \(26880\) | \(1.2833\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 8190.f have rank \(0\).
Complex multiplication
The elliptic curves in class 8190.f do not have complex multiplication.Modular form 8190.2.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.
