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SageMath
E = EllipticCurve("bb1")
E.isogeny_class()
Elliptic curves in class 32340bb
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
32340.v2 | 32340bb1 | \([0, 1, 0, -181183641, 3643311773520]\) | \(-349439858058052607328256/2844147488104248046875\) | \(-5353777725247626855468750000\) | \([2]\) | \(20966400\) | \(4.0034\) | \(\Gamma_0(N)\)-optimal |
32340.v1 | 32340bb2 | \([0, 1, 0, -4832355516, 128975649586020]\) | \(414354576760345737269208016/1182266314178222109375\) | \(35607667096768935154140000000\) | \([2]\) | \(41932800\) | \(4.3500\) |
Rank
sage: E.rank()
The elliptic curves in class 32340bb have rank \(0\).
Complex multiplication
The elliptic curves in class 32340bb do not have complex multiplication.Modular form 32340.2.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 Cremona 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 Cremona labels.