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SageMath
E = EllipticCurve("bk1")
E.isogeny_class()
Elliptic curves in class 53361bk
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 53361.bn2 | 53361bk1 | \([1, -1, 0, 185652, -116876061]\) | \(4657463/41503\) | \(-6305962295767816143\) | \([2]\) | \(829440\) | \(2.2886\) | \(\Gamma_0(N)\)-optimal |
| 53361.bn1 | 53361bk2 | \([1, -1, 0, -2749203, -1618934850]\) | \(15124197817/1294139\) | \(196631369768032812459\) | \([2]\) | \(1658880\) | \(2.6352\) |
Rank
sage: E.rank()
The elliptic curves in class 53361bk have rank \(0\).
Complex multiplication
The elliptic curves in class 53361bk do not have complex multiplication.Modular form 53361.2.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.
