Properties

 Label 25200dy Number of curves $4$ Conductor $25200$ CM no Rank $1$ Graph

Related objects

Show commands for: SageMath
sage: E = EllipticCurve("25200.cw1")

sage: E.isogeny_class()

Elliptic curves in class 25200dy

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
25200.cw4 25200dy1 [0, 0, 0, 8325, -465750] [2] 73728 $$\Gamma_0(N)$$-optimal
25200.cw3 25200dy2 [0, 0, 0, -63675, -5001750] [2, 2] 147456
25200.cw2 25200dy3 [0, 0, 0, -315675, 63794250] [2] 294912
25200.cw1 25200dy4 [0, 0, 0, -963675, -364101750] [2] 294912

Rank

sage: E.rank()

The elliptic curves in class 25200dy have rank $$1$$.

Modular form 25200.2.a.cw

sage: E.q_eigenform(10)

$$q - q^{7} + 4q^{11} + 6q^{13} + 2q^{17} + O(q^{20})$$

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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.