Properties

 Label 2800.p Number of curves $4$ Conductor $2800$ CM no Rank $1$ Graph

Related objects

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

sage: E.isogeny_class()

Elliptic curves in class 2800.p

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2800.p1 2800a3 $$[0, 0, 0, -7475, -248750]$$ $$1443468546/7$$ $$224000000$$ $$[2]$$ $$2048$$ $$0.80269$$
2800.p2 2800a4 $$[0, 0, 0, -1475, 17250]$$ $$11090466/2401$$ $$76832000000$$ $$[2]$$ $$2048$$ $$0.80269$$
2800.p3 2800a2 $$[0, 0, 0, -475, -3750]$$ $$740772/49$$ $$784000000$$ $$[2, 2]$$ $$1024$$ $$0.45611$$
2800.p4 2800a1 $$[0, 0, 0, 25, -250]$$ $$432/7$$ $$-28000000$$ $$[2]$$ $$512$$ $$0.10954$$ $$\Gamma_0(N)$$-optimal

Rank

sage: E.rank()

The elliptic curves in class 2800.p have rank $$1$$.

Complex multiplication

The elliptic curves in class 2800.p do not have complex multiplication.

Modular form2800.2.a.p

sage: E.q_eigenform(10)

$$q - q^{7} - 3q^{9} + 4q^{11} - 2q^{13} + 6q^{17} - 8q^{19} + O(q^{20})$$

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 LMFDB numbering.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.