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SageMath
E = EllipticCurve("y1")
E.isogeny_class()
Elliptic curves in class 123840y
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
123840.eh2 | 123840y1 | \([0, 0, 0, -4812, 124016]\) | \(1740992427/68800\) | \(486958694400\) | \([2]\) | \(147456\) | \(1.0095\) | \(\Gamma_0(N)\)-optimal |
123840.eh1 | 123840y2 | \([0, 0, 0, -12492, -370576]\) | \(30459021867/9245000\) | \(65435074560000\) | \([2]\) | \(294912\) | \(1.3560\) |
Rank
sage: E.rank()
The elliptic curves in class 123840y have rank \(1\).
Complex multiplication
The elliptic curves in class 123840y do not have complex multiplication.Modular form 123840.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.