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SageMath
E = EllipticCurve("s1")
E.isogeny_class()
Elliptic curves in class 138600.s
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
138600.s1 | 138600dd1 | \([0, 0, 0, -39990, -3077975]\) | \(4850878539776/130977\) | \(190964466000\) | \([2]\) | \(266240\) | \(1.2689\) | \(\Gamma_0(N)\)-optimal |
138600.s2 | 138600dd2 | \([0, 0, 0, -38415, -3331550]\) | \(-268750151696/50014503\) | \(-1166738325984000\) | \([2]\) | \(532480\) | \(1.6155\) |
Rank
sage: E.rank()
The elliptic curves in class 138600.s have rank \(1\).
Complex multiplication
The elliptic curves in class 138600.s do not have complex multiplication.Modular form 138600.2.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.