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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 122018.f
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 122018.f1 | 122018j3 | \([1, 1, 0, -5217540, 36896684752]\) | \(-69173457625/2550136832\) | \(-579088850663829854486528\) | \([]\) | \(13296960\) | \(3.2399\) | |
| 122018.f2 | 122018j1 | \([1, 1, 0, -946910, -355166612]\) | \(-413493625/152\) | \(-34516385237206808\) | \([]\) | \(1477440\) | \(2.1413\) | \(\Gamma_0(N)\)-optimal |
| 122018.f3 | 122018j2 | \([1, 1, 0, 578315, -1347844051]\) | \(94196375/3511808\) | \(-797466564520426092032\) | \([]\) | \(4432320\) | \(2.6906\) |
Rank
sage: E.rank()
The elliptic curves in class 122018.f have rank \(0\).
Complex multiplication
The elliptic curves in class 122018.f do not have complex multiplication.Modular form 122018.2.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.
\(\left(\begin{array}{rrr} 1 & 9 & 3 \\ 9 & 1 & 3 \\ 3 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
