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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 81600.g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
81600.g1 | 81600gt2 | \([0, -1, 0, -5933, 177987]\) | \(-23100424192/14739\) | \(-14739000000\) | \([]\) | \(93312\) | \(0.89207\) | |
81600.g2 | 81600gt1 | \([0, -1, 0, 67, 987]\) | \(32768/459\) | \(-459000000\) | \([]\) | \(31104\) | \(0.34276\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 81600.g have rank \(1\).
Complex multiplication
The elliptic curves in class 81600.g do not have complex multiplication.Modular form 81600.2.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.