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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 43890.g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
43890.g1 | 43890f2 | \([1, 1, 0, -3663, -83187]\) | \(5437755907485049/266077155960\) | \(266077155960\) | \([2]\) | \(76800\) | \(0.95174\) | |
43890.g2 | 43890f1 | \([1, 1, 0, 137, -4907]\) | \(281140102151/10807473600\) | \(-10807473600\) | \([2]\) | \(38400\) | \(0.60517\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 43890.g have rank \(0\).
Complex multiplication
The elliptic curves in class 43890.g do not have complex multiplication.Modular form 43890.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.