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SageMath
E = EllipticCurve("cr1")
E.isogeny_class()
Elliptic curves in class 34496.cr
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
34496.cr1 | 34496de3 | \([0, 1, 0, -1532785, -730926659]\) | \(-52893159101157376/11\) | \(-82824896\) | \([]\) | \(144000\) | \(1.8162\) | |
34496.cr2 | 34496de2 | \([0, 1, 0, -2025, -64219]\) | \(-122023936/161051\) | \(-1212639302336\) | \([]\) | \(28800\) | \(1.0115\) | |
34496.cr3 | 34496de1 | \([0, 1, 0, -65, 461]\) | \(-4096/11\) | \(-82824896\) | \([]\) | \(5760\) | \(0.20680\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 34496.cr have rank \(0\).
Complex multiplication
The elliptic curves in class 34496.cr do not have complex multiplication.Modular form 34496.2.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.
\(\left(\begin{array}{rrr} 1 & 5 & 25 \\ 5 & 1 & 5 \\ 25 & 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.