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SageMath
E = EllipticCurve("s1")
E.isogeny_class()
Elliptic curves in class 50094s
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
50094.k4 | 50094s1 | \([1, -1, 0, -75708, -14575280]\) | \(-37159393753/49741824\) | \(-64239972415635456\) | \([2]\) | \(368640\) | \(1.9179\) | \(\Gamma_0(N)\)-optimal |
50094.k3 | 50094s2 | \([1, -1, 0, -1469628, -685050800]\) | \(271808161065433/147476736\) | \(190461480716669184\) | \([2, 2]\) | \(737280\) | \(2.2644\) | |
50094.k2 | 50094s3 | \([1, -1, 0, -1730988, -424370336]\) | \(444142553850073/196663299888\) | \(253984352483193287472\) | \([2]\) | \(1474560\) | \(2.6110\) | |
50094.k1 | 50094s4 | \([1, -1, 0, -23510988, -43872891584]\) | \(1112891236915770073/327888\) | \(423456849419472\) | \([2]\) | \(1474560\) | \(2.6110\) |
Rank
sage: E.rank()
The elliptic curves in class 50094s have rank \(1\).
Complex multiplication
The elliptic curves in class 50094s do not have complex multiplication.Modular form 50094.2.a.s
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 Cremona numbering.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.