# Properties

 Label 2900.c Number of curves $2$ Conductor $2900$ CM no Rank $1$ Graph

# Related objects

Show commands: SageMath
E = EllipticCurve("c1")

E.isogeny_class()

## Elliptic curves in class 2900.c

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2900.c1 2900e1 $$[0, 0, 0, -200, -875]$$ $$3538944/725$$ $$181250000$$ $$[2]$$ $$576$$ $$0.30007$$ $$\Gamma_0(N)$$-optimal
2900.c2 2900e2 $$[0, 0, 0, 425, -5250]$$ $$2122416/4205$$ $$-16820000000$$ $$[2]$$ $$1152$$ $$0.64664$$

## Rank

sage: E.rank()

The elliptic curves in class 2900.c have rank $$1$$.

## Complex multiplication

The elliptic curves in class 2900.c do not have complex multiplication.

## Modular form2900.2.a.c

sage: E.q_eigenform(10)

$$q - 3 q^{9} - 2 q^{11} + 2 q^{13} - 2 q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.