Properties

 Label 33800y Number of curves 2 Conductor 33800 CM no Rank 1 Graph

Related objects

Show commands for: SageMath
sage: E = EllipticCurve("33800.p1")

sage: E.isogeny_class()

Elliptic curves in class 33800y

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
33800.p2 33800y1 [0, 0, 0, -147875, -13731250] [2] 268800 $$\Gamma_0(N)$$-optimal
33800.p1 33800y2 [0, 0, 0, -992875, 370743750] [2] 537600

Rank

sage: E.rank()

The elliptic curves in class 33800y have rank $$1$$.

Modular form 33800.2.a.p

sage: E.q_eigenform(10)

$$q + 4q^{7} - 3q^{9} + 2q^{11} - 4q^{17} + 2q^{19} + O(q^{20})$$

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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.