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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 40931.a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
40931.a1 | 40931a3 | \([0, -1, 1, -29099460, -60409576035]\) | \(-52893159101157376/11\) | \(-566724117971\) | \([]\) | \(1110000\) | \(2.5521\) | |
40931.a2 | 40931a2 | \([0, -1, 1, -38450, -5243475]\) | \(-122023936/161051\) | \(-8297407811213411\) | \([]\) | \(222000\) | \(1.7474\) | |
40931.a3 | 40931a1 | \([0, -1, 1, -1240, 40345]\) | \(-4096/11\) | \(-566724117971\) | \([]\) | \(44400\) | \(0.94271\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 40931.a have rank \(1\).
Complex multiplication
The elliptic curves in class 40931.a do not have complex multiplication.Modular form 40931.2.a.a
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.