Properties

 Label 53361bj Number of curves 4 Conductor 53361 CM no Rank 0 Graph

Related objects

Show commands for: SageMath
sage: E = EllipticCurve("53361.bm1")
sage: E.isogeny_class()

Elliptic curves in class 53361bj

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
53361.bm3 53361bj1 [1, -1, 0, -347958, 78425199] 2 414720 $$\Gamma_0(N)$$-optimal
53361.bm2 53361bj2 [1, -1, 0, -614763, -58125600] 4 829440
53361.bm4 53361bj3 [1, -1, 0, 2320092, -454331025] 2 1658880
53361.bm1 53361bj4 [1, -1, 0, -7818498, -8404372971] 2 1658880

Rank

sage: E.rank()

The elliptic curves in class 53361bj have rank $$0$$.

Modular form 53361.2.a.bm

sage: E.q_eigenform(10)
$$q + q^{2} - q^{4} - 2q^{5} - 3q^{8} - 2q^{10} - 2q^{13} - q^{16} + 2q^{17} + O(q^{20})$$

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.

$$\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)$$

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)

The vertices are labelled with Cremona labels.