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SageMath
E = EllipticCurve("fq1")
E.isogeny_class()
Elliptic curves in class 92400.fq
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
92400.fq1 | 92400gm4 | \([0, 1, 0, -19712008, 33679039988]\) | \(13235378341603461121/9240\) | \(591360000000\) | \([2]\) | \(1769472\) | \(2.4718\) | |
92400.fq2 | 92400gm2 | \([0, 1, 0, -1232008, 525919988]\) | \(3231355012744321/85377600\) | \(5464166400000000\) | \([2, 2]\) | \(884736\) | \(2.1253\) | |
92400.fq3 | 92400gm3 | \([0, 1, 0, -1184008, 568831988]\) | \(-2868190647517441/527295615000\) | \(-33746919360000000000\) | \([2]\) | \(1769472\) | \(2.4718\) | |
92400.fq4 | 92400gm1 | \([0, 1, 0, -80008, 7519988]\) | \(885012508801/127733760\) | \(8174960640000000\) | \([2]\) | \(442368\) | \(1.7787\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 92400.fq have rank \(0\).
Complex multiplication
The elliptic curves in class 92400.fq do not have complex multiplication.Modular form 92400.2.a.fq
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.