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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 1936.i
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
1936.i1 | 1936g3 | \([0, 1, 0, -15140165, -22679876749]\) | \(-52893159101157376/11\) | \(-79819452416\) | \([]\) | \(24000\) | \(2.3888\) | |
1936.i2 | 1936g2 | \([0, 1, 0, -20005, -1979309]\) | \(-122023936/161051\) | \(-1168636602822656\) | \([]\) | \(4800\) | \(1.5841\) | |
1936.i3 | 1936g1 | \([0, 1, 0, -645, 14771]\) | \(-4096/11\) | \(-79819452416\) | \([]\) | \(960\) | \(0.77937\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 1936.i have rank \(1\).
Complex multiplication
The elliptic curves in class 1936.i do not have complex multiplication.Modular form 1936.2.a.i
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.
\(\left(\begin{array}{rrr} 1 & 5 & 25 \\ 5 & 1 & 5 \\ 25 & 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.