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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 140790.e
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
140790.e1 | 140790cu3 | \([1, 1, 0, -75137103, 251879496807]\) | \(-997161390145682805889/5653381347656250\) | \(-265968306129455566406250\) | \([]\) | \(25194240\) | \(3.3369\) | |
140790.e2 | 140790cu1 | \([1, 1, 0, -290973, -102232323]\) | \(-57911193276769/62229772800\) | \(-2927654485805836800\) | \([]\) | \(2799360\) | \(2.2383\) | \(\Gamma_0(N)\)-optimal |
140790.e3 | 140790cu2 | \([1, 1, 0, 2438187, 1842567093]\) | \(34072410714499871/50858627625000\) | \(-2392688943069062625000\) | \([]\) | \(8398080\) | \(2.7876\) |
Rank
sage: E.rank()
The elliptic curves in class 140790.e have rank \(0\).
Complex multiplication
The elliptic curves in class 140790.e do not have complex multiplication.Modular form 140790.2.a.e
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.