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SageMath
E = EllipticCurve("cr1")
E.isogeny_class()
Elliptic curves in class 166410.cr
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
166410.cr1 | 166410v2 | \([1, -1, 1, -360902, 57635901]\) | \(30459021867/9245000\) | \(1577907037476135000\) | \([2]\) | \(2838528\) | \(2.1969\) | |
166410.cr2 | 166410v1 | \([1, -1, 1, -139022, -19223331]\) | \(1740992427/68800\) | \(11742563999822400\) | \([2]\) | \(1419264\) | \(1.8503\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 166410.cr have rank \(0\).
Complex multiplication
The elliptic curves in class 166410.cr do not have complex multiplication.Modular form 166410.2.a.cr
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.