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SageMath
E = EllipticCurve("dd1")
E.isogeny_class()
Elliptic curves in class 462825dd
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
462825.dd1 | 462825dd1 | \([0, 0, 1, -358153950, 2608874923531]\) | \(-251784668965666816/353546875\) | \(-7134288509414794921875\) | \([]\) | \(101191680\) | \(3.4656\) | \(\Gamma_0(N)\)-optimal |
462825.dd2 | 462825dd2 | \([0, 0, 1, -262866450, 4027300826656]\) | \(-99546392709922816/289614925147075\) | \(-5844193737059062133448046875\) | \([]\) | \(303575040\) | \(4.0149\) |
Rank
sage: E.rank()
The elliptic curves in class 462825dd have rank \(0\).
Complex multiplication
The elliptic curves in class 462825dd do not have complex multiplication.Modular form 462825.2.a.dd
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.