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SageMath
E = EllipticCurve("er1")
E.isogeny_class()
Elliptic curves in class 310464.er
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 310464.er1 | 310464er2 | \([0, 0, 0, -40205676, -68823498800]\) | \(1278763167594532/375974556419\) | \(2113265945723095003889664\) | \([2]\) | \(35389440\) | \(3.3734\) | |
| 310464.er2 | 310464er1 | \([0, 0, 0, 6752004, -7158673424]\) | \(24226243449392/29774625727\) | \(-41839069639992851939328\) | \([2]\) | \(17694720\) | \(3.0268\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 310464.er have rank \(1\).
Complex multiplication
The elliptic curves in class 310464.er do not have complex multiplication.Modular form 310464.2.a.er
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.
