Properties

 Label 33800b Number of curves 4 Conductor 33800 CM no Rank 1 Graph

Related objects

Show commands for: SageMath
sage: E = EllipticCurve("33800.m1")

sage: E.isogeny_class()

Elliptic curves in class 33800b

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
33800.m3 33800b1 [0, 0, 0, -8450, 274625] [2] 55296 $$\Gamma_0(N)$$-optimal
33800.m2 33800b2 [0, 0, 0, -29575, -1647750] [2, 2] 110592
33800.m4 33800b3 [0, 0, 0, 54925, -9337250] [2] 221184
33800.m1 33800b4 [0, 0, 0, -452075, -116990250] [2] 221184

Rank

sage: E.rank()

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

Modular form 33800.2.a.m

sage: E.q_eigenform(10)

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

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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.