# Properties

 Label 4004.c Number of curves 2 Conductor 4004 CM no Rank 0 Graph

# Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("4004.c1")

sage: E.isogeny_class()

## Elliptic curves in class 4004.c

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
4004.c1 4004c1 [0, -1, 0, -21, 38] [2] 840 $$\Gamma_0(N)$$-optimal
4004.c2 4004c2 [0, -1, 0, 44, 168] [2] 1680

## Rank

sage: E.rank()

The elliptic curves in class 4004.c have rank $$0$$.

## Modular form4004.2.a.c

sage: E.q_eigenform(10)

$$q + 2q^{3} + 4q^{5} + q^{7} + q^{9} + q^{11} - q^{13} + 8q^{15} + 2q^{17} + 4q^{19} + O(q^{20})$$

## 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.