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SageMath
E = EllipticCurve("z1")
E.isogeny_class()
Elliptic curves in class 2800.z
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
2800.z1 | 2800s3 | \([0, 1, 0, -52533, 4830563]\) | \(-250523582464/13671875\) | \(-875000000000000\) | \([]\) | \(10368\) | \(1.6253\) | |
2800.z2 | 2800s1 | \([0, 1, 0, -533, -5437]\) | \(-262144/35\) | \(-2240000000\) | \([]\) | \(1152\) | \(0.52672\) | \(\Gamma_0(N)\)-optimal |
2800.z3 | 2800s2 | \([0, 1, 0, 3467, 14563]\) | \(71991296/42875\) | \(-2744000000000\) | \([]\) | \(3456\) | \(1.0760\) |
Rank
sage: E.rank()
The elliptic curves in class 2800.z have rank \(1\).
Complex multiplication
The elliptic curves in class 2800.z do not have complex multiplication.Modular form 2800.2.a.z
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.
\(\left(\begin{array}{rrr} 1 & 9 & 3 \\ 9 & 1 & 3 \\ 3 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.