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SageMath
E = EllipticCurve("ey1")
E.isogeny_class()
Elliptic curves in class 107712ey
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
107712.dd1 | 107712ey1 | \([0, 0, 0, -47100, 3930352]\) | \(967473250000/1153977\) | \(13783027433472\) | \([2]\) | \(245760\) | \(1.4324\) | \(\Gamma_0(N)\)-optimal |
107712.dd2 | 107712ey2 | \([0, 0, 0, -34860, 6020944]\) | \(-98061470500/271048833\) | \(-12949559656906752\) | \([2]\) | \(491520\) | \(1.7789\) |
Rank
sage: E.rank()
The elliptic curves in class 107712ey have rank \(1\).
Complex multiplication
The elliptic curves in class 107712ey do not have complex multiplication.Modular form 107712.2.a.ey
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 Cremona 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 Cremona labels.