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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 36300.g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
36300.g1 | 36300p2 | \([0, -1, 0, -1102108, -444965288]\) | \(-2527934627152/9\) | \(-527076000000\) | \([]\) | \(326592\) | \(1.8911\) | |
36300.g2 | 36300p1 | \([0, -1, 0, -13108, -653288]\) | \(-4253392/729\) | \(-42693156000000\) | \([]\) | \(108864\) | \(1.3418\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 36300.g have rank \(1\).
Complex multiplication
The elliptic curves in class 36300.g do not have complex multiplication.Modular form 36300.2.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.