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SageMath
E = EllipticCurve("cb1")
E.isogeny_class()
Elliptic curves in class 28050cb
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
28050.cn1 | 28050cb1 | \([1, 1, 1, -2563, 49781]\) | \(-119168121961/2524500\) | \(-39445312500\) | \([]\) | \(34560\) | \(0.82361\) | \(\Gamma_0(N)\)-optimal |
28050.cn2 | 28050cb2 | \([1, 1, 1, 10562, 233531]\) | \(8339492177639/6277634880\) | \(-98088045000000\) | \([]\) | \(103680\) | \(1.3729\) |
Rank
sage: E.rank()
The elliptic curves in class 28050cb have rank \(1\).
Complex multiplication
The elliptic curves in class 28050cb do not have complex multiplication.Modular form 28050.2.a.cb
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 Cremona 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 Cremona labels.