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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 10890.g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
10890.g1 | 10890b2 | \([1, -1, 0, -42675, -1311139]\) | \(2037123/1000\) | \(4219225854723000\) | \([]\) | \(76032\) | \(1.6915\) | |
10890.g2 | 10890b1 | \([1, -1, 0, -22710, 1322910]\) | \(223810587/10\) | \(57876897870\) | \([3]\) | \(25344\) | \(1.1421\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 10890.g have rank \(0\).
Complex multiplication
The elliptic curves in class 10890.g do not have complex multiplication.Modular form 10890.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.