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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 348075.n
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 348075.n1 | 348075n1 | \([1, -1, 1, -102380, -12576378]\) | \(10418796526321/6390657\) | \(72793577390625\) | \([2]\) | \(1433600\) | \(1.6027\) | \(\Gamma_0(N)\)-optimal |
| 348075.n2 | 348075n2 | \([1, -1, 1, -83255, -17434128]\) | \(-5602762882081/8312741073\) | \(-94687316284640625\) | \([2]\) | \(2867200\) | \(1.9492\) |
Rank
sage: E.rank()
The elliptic curves in class 348075.n have rank \(1\).
Complex multiplication
The elliptic curves in class 348075.n do not have complex multiplication.Modular form 348075.2.a.n
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.
