# Properties

 Label 2576.c Number of curves $2$ Conductor $2576$ CM no Rank $1$ Graph

# Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 2576.c

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2576.c1 2576n2 $$[0, 1, 0, -9688, -346860]$$ $$24553362849625/1755162752$$ $$7189146632192$$ $$[2]$$ $$5376$$ $$1.2139$$
2576.c2 2576n1 $$[0, 1, 0, 552, -23276]$$ $$4533086375/60669952$$ $$-248504123392$$ $$[2]$$ $$2688$$ $$0.86733$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 2576.c have rank $$1$$.

## Complex multiplication

The elliptic curves in class 2576.c do not have complex multiplication.

## Modular form2576.2.a.c

sage: E.q_eigenform(10)

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

## 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.