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SageMath
E = EllipticCurve("bk1")
E.isogeny_class()
Elliptic curves in class 167310.bk
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 167310.bk1 | 167310dc2 | \([1, -1, 0, -3372849, -2383359107]\) | \(1205943158724121/1258400\) | \(4427987148842400\) | \([2]\) | \(3870720\) | \(2.2921\) | |
| 167310.bk2 | 167310dc1 | \([1, -1, 0, -209169, -37806755]\) | \(-287626699801/9518080\) | \(-33491684616698880\) | \([2]\) | \(1935360\) | \(1.9455\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 167310.bk have rank \(1\).
Complex multiplication
The elliptic curves in class 167310.bk do not have complex multiplication.Modular form 167310.2.a.bk
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.
