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SageMath
E = EllipticCurve("v1")
E.isogeny_class()
Elliptic curves in class 4410.v
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
4410.v1 | 4410bg1 | \([1, -1, 1, -471218, -70884943]\) | \(393349474783/153600000\) | \(4518570931660800000\) | \([2]\) | \(125440\) | \(2.2783\) | \(\Gamma_0(N)\)-optimal |
4410.v2 | 4410bg2 | \([1, -1, 1, 1504462, -511856719]\) | \(12801408679457/11250000000\) | \(-330950019408750000000\) | \([2]\) | \(250880\) | \(2.6248\) |
Rank
sage: E.rank()
The elliptic curves in class 4410.v have rank \(0\).
Complex multiplication
The elliptic curves in class 4410.v do not have complex multiplication.Modular form 4410.2.a.v
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.