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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 2352.f
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 2352.f1 | 2352l2 | \([0, -1, 0, -2256, -42048]\) | \(-6329617441/279936\) | \(-56184274944\) | \([]\) | \(2016\) | \(0.82762\) | |
| 2352.f2 | 2352l1 | \([0, -1, 0, -16, 64]\) | \(-2401/6\) | \(-1204224\) | \([]\) | \(288\) | \(-0.14533\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 2352.f have rank \(1\).
Complex multiplication
The elliptic curves in class 2352.f do not have complex multiplication.Modular form 2352.2.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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
