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SageMath
E = EllipticCurve("s1")
E.isogeny_class()
Elliptic curves in class 40898s
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
40898.h2 | 40898s1 | \([1, 0, 1, 503, 1692]\) | \(24167/16\) | \(-9344702224\) | \([]\) | \(32832\) | \(0.60196\) | \(\Gamma_0(N)\)-optimal |
40898.h1 | 40898s2 | \([1, 0, 1, -8792, 325158]\) | \(-128667913/4096\) | \(-2392243769344\) | \([]\) | \(98496\) | \(1.1513\) |
Rank
sage: E.rank()
The elliptic curves in class 40898s have rank \(0\).
Complex multiplication
The elliptic curves in class 40898s do not have complex multiplication.Modular form 40898.2.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 Cremona 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 Cremona labels.