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SageMath
E = EllipticCurve("v1")
E.isogeny_class()
Elliptic curves in class 42483.v
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
42483.v1 | 42483r2 | \([1, 0, 1, -1550925, -742233089]\) | \(423564751/867\) | \(844490922904319061\) | \([2]\) | \(1032192\) | \(2.3261\) | |
42483.v2 | 42483r1 | \([1, 0, 1, -64020, -19597259]\) | \(-29791/153\) | \(-149027809924291599\) | \([2]\) | \(516096\) | \(1.9795\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 42483.v have rank \(1\).
Complex multiplication
The elliptic curves in class 42483.v do not have complex multiplication.Modular form 42483.2.a.v
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 LMFDB 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 LMFDB labels.