# Properties

 Label 5776.c Number of curves $3$ Conductor $5776$ CM no Rank $1$ Graph

# Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 5776.c

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
5776.c1 5776q3 $$[0, 1, 0, -4443669, -3606941501]$$ $$-50357871050752/19$$ $$-3661298642944$$ $$[]$$ $$77760$$ $$2.1988$$
5776.c2 5776q2 $$[0, 1, 0, -53909, -5143421]$$ $$-89915392/6859$$ $$-1321728810102784$$ $$[]$$ $$25920$$ $$1.6495$$
5776.c3 5776q1 $$[0, 1, 0, 3851, -2781]$$ $$32768/19$$ $$-3661298642944$$ $$[]$$ $$8640$$ $$1.1002$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 5776.c have rank $$1$$.

## Complex multiplication

The elliptic curves in class 5776.c do not have complex multiplication.

## Modular form5776.2.a.c

sage: E.q_eigenform(10)

$$q - 2q^{3} + 3q^{5} + q^{7} + q^{9} - 3q^{11} + 4q^{13} - 6q^{15} - 3q^{17} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.