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SageMath
E = EllipticCurve("s1")
E.isogeny_class()
Elliptic curves in class 355488s
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
355488.s2 | 355488s1 | \([0, -1, 0, 882, -56172]\) | \(8000/147\) | \(-1392721643712\) | \([2]\) | \(380160\) | \(1.0106\) | \(\Gamma_0(N)\)-optimal |
355488.s1 | 355488s2 | \([0, -1, 0, -17633, -844911]\) | \(1000000/63\) | \(38200365084672\) | \([2]\) | \(760320\) | \(1.3572\) |
Rank
sage: E.rank()
The elliptic curves in class 355488s have rank \(1\).
Complex multiplication
The elliptic curves in class 355488s do not have complex multiplication.Modular form 355488.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.