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SageMath
E = EllipticCurve("dr1")
E.isogeny_class()
Elliptic curves in class 360640.dr
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
360640.dr1 | 360640dr1 | \([0, 0, 0, -510188, 140212912]\) | \(476196576129/197225\) | \(6082612173209600\) | \([2]\) | \(3538944\) | \(1.9907\) | \(\Gamma_0(N)\)-optimal |
360640.dr2 | 360640dr2 | \([0, 0, 0, -431788, 184775472]\) | \(-288673724529/311181605\) | \(-9597145486890106880\) | \([2]\) | \(7077888\) | \(2.3372\) |
Rank
sage: E.rank()
The elliptic curves in class 360640.dr have rank \(1\).
Complex multiplication
The elliptic curves in class 360640.dr do not have complex multiplication.Modular form 360640.2.a.dr
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.