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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 570.g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
570.g1 | 570g3 | \([1, 1, 1, -621, -6207]\) | \(26487576322129/44531250\) | \(44531250\) | \([2]\) | \(256\) | \(0.36292\) | |
570.g2 | 570g2 | \([1, 1, 1, -51, -51]\) | \(14688124849/8122500\) | \(8122500\) | \([2, 2]\) | \(128\) | \(0.016344\) | |
570.g3 | 570g1 | \([1, 1, 1, -31, 53]\) | \(3301293169/22800\) | \(22800\) | \([4]\) | \(64\) | \(-0.33023\) | \(\Gamma_0(N)\)-optimal |
570.g4 | 570g4 | \([1, 1, 1, 199, -151]\) | \(871257511151/527800050\) | \(-527800050\) | \([2]\) | \(256\) | \(0.36292\) |
Rank
sage: E.rank()
The elliptic curves in class 570.g have rank \(0\).
Complex multiplication
The elliptic curves in class 570.g do not have complex multiplication.Modular form 570.2.a.g
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.