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SageMath
E = EllipticCurve("bz1")
E.isogeny_class()
Elliptic curves in class 277350.bz
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
277350.bz1 | 277350bz2 | \([1, 1, 1, -7662996563, 258190358067281]\) | \(503835593418244309249/898614000000\) | \(88757270858032593750000000\) | \([2]\) | \(447068160\) | \(4.2373\) | |
277350.bz2 | 277350bz1 | \([1, 1, 1, -474084563, 4119830163281]\) | \(-119305480789133569/5200091136000\) | \(-513619749352231776000000000\) | \([2]\) | \(223534080\) | \(3.8907\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 277350.bz have rank \(1\).
Complex multiplication
The elliptic curves in class 277350.bz do not have complex multiplication.Modular form 277350.2.a.bz
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.