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SageMath
E = EllipticCurve("y1")
E.isogeny_class()
Elliptic curves in class 355740y
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
355740.y2 | 355740y1 | \([0, -1, 0, 9804590, -20137404923]\) | \(2134896896/4822335\) | \(-235446615088839489590640\) | \([]\) | \(41057280\) | \(3.1688\) | \(\Gamma_0(N)\)-optimal |
355740.y1 | 355740y2 | \([0, -1, 0, -377596270, -2831970326975]\) | \(-121947169848064/397065375\) | \(-19386396530463086917254000\) | \([]\) | \(123171840\) | \(3.7181\) |
Rank
sage: E.rank()
The elliptic curves in class 355740y have rank \(1\).
Complex multiplication
The elliptic curves in class 355740y do not have complex multiplication.Modular form 355740.2.a.y
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.