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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 3950.g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
3950.g1 | 3950h3 | \([1, 1, 1, -130413, -18181469]\) | \(15698803397448457/20709376\) | \(323584000000\) | \([]\) | \(12960\) | \(1.4846\) | |
3950.g2 | 3950h2 | \([1, 1, 1, -2038, -11469]\) | \(59914169497/31554496\) | \(493039000000\) | \([]\) | \(4320\) | \(0.93527\) | |
3950.g3 | 3950h1 | \([1, 1, 1, -1163, 14781]\) | \(11134383337/316\) | \(4937500\) | \([]\) | \(1440\) | \(0.38596\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 3950.g have rank \(1\).
Complex multiplication
The elliptic curves in class 3950.g do not have complex multiplication.Modular form 3950.2.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.