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SageMath
E = EllipticCurve("s1")
E.isogeny_class()
Elliptic curves in class 490245.s
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
490245.s1 | 490245s1 | \([1, 0, 0, -1961, -33384]\) | \(7088952961/50025\) | \(5885391225\) | \([2]\) | \(589824\) | \(0.70731\) | \(\Gamma_0(N)\)-optimal |
490245.s2 | 490245s2 | \([1, 0, 0, -736, -74299]\) | \(-374805361/20020005\) | \(-2355333568245\) | \([2]\) | \(1179648\) | \(1.0539\) |
Rank
sage: E.rank()
The elliptic curves in class 490245.s have rank \(0\).
Complex multiplication
The elliptic curves in class 490245.s do not have complex multiplication.Modular form 490245.2.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.