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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 5610.i
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
5610.i1 | 5610g2 | \([1, 1, 0, -185702, -30879084]\) | \(708234550511150304361/23696640000\) | \(23696640000\) | \([2]\) | \(28160\) | \(1.4903\) | |
5610.i2 | 5610g1 | \([1, 1, 0, -11622, -484716]\) | \(173629978755828841/1000026931200\) | \(1000026931200\) | \([2]\) | \(14080\) | \(1.1437\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 5610.i have rank \(0\).
Complex multiplication
The elliptic curves in class 5610.i do not have complex multiplication.Modular form 5610.2.a.i
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.