Properties

 Label 17600cd Number of curves 3 Conductor 17600 CM no Rank 1 Graph

Related objects

Show commands for: SageMath
sage: E = EllipticCurve("17600.cd1")

sage: E.isogeny_class()

Elliptic curves in class 17600cd

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
17600.cd3 17600cd1 [0, 1, 0, -33, -187] [] 2240 $$\Gamma_0(N)$$-optimal
17600.cd2 17600cd2 [0, 1, 0, -1033, 22813] [] 11200
17600.cd1 17600cd3 [0, 1, 0, -782033, 265925813] [] 56000

Rank

sage: E.rank()

The elliptic curves in class 17600cd have rank $$1$$.

Modular form 17600.2.a.cd

sage: E.q_eigenform(10)

$$q + q^{3} - 2q^{7} - 2q^{9} + q^{11} + 4q^{13} + 2q^{17} + O(q^{20})$$

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.

$$\left(\begin{array}{rrr} 1 & 5 & 25 \\ 5 & 1 & 5 \\ 25 & 5 & 1 \end{array}\right)$$

Isogeny graph

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

The vertices are labelled with Cremona labels.