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SageMath
E = EllipticCurve("bj1")
E.isogeny_class()
Elliptic curves in class 24882bj
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
24882.bi2 | 24882bj1 | \([1, 0, 0, 411779, 8250737]\) | \(7721758769769063671471/4497774542859970944\) | \(-4497774542859970944\) | \([7]\) | \(482944\) | \(2.2686\) | \(\Gamma_0(N)\)-optimal |
24882.bi1 | 24882bj2 | \([1, 0, 0, -163046131, -801348432313]\) | \(-479352730263827621784814619569/214316023050990383094\) | \(-214316023050990383094\) | \([]\) | \(3380608\) | \(3.2416\) |
Rank
sage: E.rank()
The elliptic curves in class 24882bj have rank \(1\).
Complex multiplication
The elliptic curves in class 24882bj do not have complex multiplication.Modular form 24882.2.a.bj
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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.