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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 574.i
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
574.i1 | 574j2 | \([1, 1, 1, -15785, -769911]\) | \(434969885624052241/1621986814\) | \(1621986814\) | \([]\) | \(600\) | \(0.98275\) | |
574.i2 | 574j1 | \([1, 1, 1, -175, 789]\) | \(592915705201/22050784\) | \(22050784\) | \([5]\) | \(120\) | \(0.17803\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 574.i have rank \(0\).
Complex multiplication
The elliptic curves in class 574.i do not have complex multiplication.Modular form 574.2.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.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.