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SageMath
E = EllipticCurve("cr1")
E.isogeny_class()
Elliptic curves in class 28050.cr
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
28050.cr1 | 28050ci2 | \([1, 1, 1, -30663, -1206219]\) | \(204055591784617/78708537864\) | \(1229820904125000\) | \([2]\) | \(172032\) | \(1.5945\) | |
28050.cr2 | 28050ci1 | \([1, 1, 1, -13663, 595781]\) | \(18052771191337/444958272\) | \(6952473000000\) | \([2]\) | \(86016\) | \(1.2479\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 28050.cr have rank \(0\).
Complex multiplication
The elliptic curves in class 28050.cr do not have complex multiplication.Modular form 28050.2.a.cr
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.