Properties

 Label 51600cx Number of curves $4$ Conductor $51600$ CM no Rank $1$ Graph

Related objects

Show commands for: SageMath
sage: E = EllipticCurve("cx1")

sage: E.isogeny_class()

Elliptic curves in class 51600cx

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
51600.dv3 51600cx1 [0, 1, 0, -27408, 1735188] [2] 110592 $$\Gamma_0(N)$$-optimal
51600.dv2 51600cx2 [0, 1, 0, -35408, 631188] [2, 2] 221184
51600.dv4 51600cx3 [0, 1, 0, 136592, 5103188] [2] 442368
51600.dv1 51600cx4 [0, 1, 0, -335408, -74368812] [2] 442368

Rank

sage: E.rank()

The elliptic curves in class 51600cx have rank $$1$$.

Complex multiplication

The elliptic curves in class 51600cx do not have complex multiplication.

Modular form 51600.2.a.cx

sage: E.q_eigenform(10)

$$q + q^{3} + 4q^{7} + q^{9} + 2q^{13} - 2q^{17} - 4q^{19} + O(q^{20})$$

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.