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SageMath
E = EllipticCurve("s1")
E.isogeny_class()
Elliptic curves in class 38115.s
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
38115.s1 | 38115x2 | \([0, 0, 1, -916212, -337568553]\) | \(-65860951343104/3493875\) | \(-4512227650189875\) | \([]\) | \(414720\) | \(2.0716\) | |
38115.s2 | 38115x1 | \([0, 0, 1, -1452, -1234170]\) | \(-262144/509355\) | \(-657815667349995\) | \([]\) | \(138240\) | \(1.5223\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 38115.s have rank \(0\).
Complex multiplication
The elliptic curves in class 38115.s do not have complex multiplication.Modular form 38115.2.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.