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SageMath
E = EllipticCurve("s1")
E.isogeny_class()
Elliptic curves in class 4290.s
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
4290.s1 | 4290q2 | \([1, 1, 1, -4556, 116093]\) | \(10458774902616769/38228327280\) | \(38228327280\) | \([2]\) | \(6144\) | \(0.89116\) | |
4290.s2 | 4290q1 | \([1, 1, 1, -156, 3453]\) | \(-420021471169/5104070400\) | \(-5104070400\) | \([2]\) | \(3072\) | \(0.54459\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 4290.s have rank \(1\).
Complex multiplication
The elliptic curves in class 4290.s do not have complex multiplication.Modular form 4290.2.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 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.