# Properties

 Label 2800.m Number of curves $4$ Conductor $2800$ CM no Rank $0$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("2800.m1")

sage: E.isogeny_class()

## Elliptic curves in class 2800.m

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
2800.m1 2800o4 [0, 0, 0, -107075, 13485250]  9216
2800.m2 2800o3 [0, 0, 0, -35075, -2362750]  9216
2800.m3 2800o2 [0, 0, 0, -7075, 185250] [2, 2] 4608
2800.m4 2800o1 [0, 0, 0, 925, 17250]  2304 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 2800.m have rank $$0$$.

## Modular form2800.2.a.m

sage: E.q_eigenform(10)

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

## 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 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. 