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SageMath
E = EllipticCurve("s1")
E.isogeny_class()
Elliptic curves in class 1350.s
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
1350.s1 | 1350l2 | \([1, -1, 1, -650, -6263]\) | \(-6847995/64\) | \(-283435200\) | \([]\) | \(648\) | \(0.44358\) | |
1350.s2 | 1350l1 | \([1, -1, 1, 25, -53]\) | \(3645/4\) | \(-1968300\) | \([]\) | \(216\) | \(-0.10573\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 1350.s have rank \(0\).
Complex multiplication
The elliptic curves in class 1350.s do not have complex multiplication.Modular form 1350.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.