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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 57475.g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
57475.g1 | 57475h3 | \([0, -1, 1, -2327233, 1367270618]\) | \(-50357871050752/19\) | \(-525932171875\) | \([]\) | \(437400\) | \(2.0371\) | |
57475.g2 | 57475h2 | \([0, -1, 1, -28233, 1951993]\) | \(-89915392/6859\) | \(-189861514046875\) | \([]\) | \(145800\) | \(1.4878\) | |
57475.g3 | 57475h1 | \([0, -1, 1, 2017, 868]\) | \(32768/19\) | \(-525932171875\) | \([]\) | \(48600\) | \(0.93849\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 57475.g have rank \(0\).
Complex multiplication
The elliptic curves in class 57475.g do not have complex multiplication.Modular form 57475.2.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.
\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.