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SageMath
E = EllipticCurve("bb1")
E.isogeny_class()
Elliptic curves in class 179776.bb
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
179776.bb1 | 179776m2 | \([0, 1, 0, -96273793, 363556597375]\) | \(-6046458625/2\) | \(-32642008566391635968\) | \([]\) | \(9891072\) | \(3.1029\) | |
179776.bb2 | 179776m1 | \([0, 1, 0, -992513, 668314367]\) | \(-6625/8\) | \(-130568034265566543872\) | \([]\) | \(3297024\) | \(2.5536\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 179776.bb have rank \(1\).
Complex multiplication
The elliptic curves in class 179776.bb do not have complex multiplication.Modular form 179776.2.a.bb
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.