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SageMath
E = EllipticCurve("cd1")
E.isogeny_class()
Elliptic curves in class 115600.cd
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
115600.cd1 | 115600co2 | \([0, 1, 0, -1360708, 632550088]\) | \(-115431760/4913\) | \(-11858787649700000000\) | \([]\) | \(1244160\) | \(2.4262\) | |
115600.cd2 | 115600co1 | \([0, 1, 0, 84292, 2530088]\) | \(27440/17\) | \(-41033867300000000\) | \([]\) | \(414720\) | \(1.8769\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 115600.cd have rank \(1\).
Complex multiplication
The elliptic curves in class 115600.cd do not have complex multiplication.Modular form 115600.2.a.cd
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.