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SageMath
E = EllipticCurve("bb1")
E.isogeny_class()
Elliptic curves in class 435120.bb
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
435120.bb1 | 435120bb2 | \([0, -1, 0, -25082136, 48358115856]\) | \(7242676576090759442/11981002005\) | \(2886764349207029760\) | \([2]\) | \(24772608\) | \(2.8049\) | \(\Gamma_0(N)\)-optimal* |
435120.bb2 | 435120bb1 | \([0, -1, 0, -1552336, 771448336]\) | \(-3433942216615684/143975904975\) | \(-17345148154269465600\) | \([2]\) | \(12386304\) | \(2.4584\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 435120.bb have rank \(0\).
Complex multiplication
The elliptic curves in class 435120.bb do not have complex multiplication.Modular form 435120.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.