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SageMath
E = EllipticCurve("bp1")
E.isogeny_class()
Elliptic curves in class 17136bp
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
17136.l1 | 17136bp1 | \([0, 0, 0, -3036, -64325]\) | \(265327034368/297381\) | \(3468651984\) | \([2]\) | \(11520\) | \(0.74465\) | \(\Gamma_0(N)\)-optimal |
17136.l2 | 17136bp2 | \([0, 0, 0, -2271, -97526]\) | \(-6940769488/18000297\) | \(-3359287427328\) | \([2]\) | \(23040\) | \(1.0912\) |
Rank
sage: E.rank()
The elliptic curves in class 17136bp have rank \(1\).
Complex multiplication
The elliptic curves in class 17136bp do not have complex multiplication.Modular form 17136.2.a.bp
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.