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SageMath
E = EllipticCurve("dy1")
E.isogeny_class()
Elliptic curves in class 129360dy
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
129360.o2 | 129360dy1 | \([0, -1, 0, -1536445976, -23172050234640]\) | \(2426796094451411844127/969756530688000\) | \(160289480397074397659136000\) | \([2]\) | \(72253440\) | \(3.9920\) | \(\Gamma_0(N)\)-optimal |
129360.o1 | 129360dy2 | \([0, -1, 0, -24580777496, -1483334637202704]\) | \(9937296563535244838593567/1587762000000\) | \(262438599710859264000000\) | \([2]\) | \(144506880\) | \(4.3386\) |
Rank
sage: E.rank()
The elliptic curves in class 129360dy have rank \(1\).
Complex multiplication
The elliptic curves in class 129360dy do not have complex multiplication.Modular form 129360.2.a.dy
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.