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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 8470g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
8470.d2 | 8470g1 | \([1, 0, 1, 41, 42]\) | \(5929741/3920\) | \(-5217520\) | \([2]\) | \(2304\) | \(-0.022244\) | \(\Gamma_0(N)\)-optimal |
8470.d1 | 8470g2 | \([1, 0, 1, -179, 306]\) | \(472729139/240100\) | \(319573100\) | \([2]\) | \(4608\) | \(0.32433\) |
Rank
sage: E.rank()
The elliptic curves in class 8470g have rank \(2\).
Complex multiplication
The elliptic curves in class 8470g do not have complex multiplication.Modular form 8470.2.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 Cremona 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 Cremona labels.