Show commands:
SageMath
E = EllipticCurve("bk1")
E.isogeny_class()
Elliptic curves in class 37026bk
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
37026.ba2 | 37026bk1 | \([1, -1, 1, -448436066, -3513135473823]\) | \(7722211175253055152433/340131399900069888\) | \(439268808222070061213417472\) | \([2]\) | \(15575040\) | \(3.8753\) | \(\Gamma_0(N)\)-optimal |
37026.ba1 | 37026bk2 | \([1, -1, 1, -1206728546, 11501662264161]\) | \(150476552140919246594353/42832838728685592576\) | \(55317239239440124283688198144\) | \([2]\) | \(31150080\) | \(4.2219\) |
Rank
sage: E.rank()
The elliptic curves in class 37026bk have rank \(1\).
Complex multiplication
The elliptic curves in class 37026bk do not have complex multiplication.Modular form 37026.2.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 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.