# Properties

 Label 784c Number of curves $4$ Conductor $784$ CM no Rank $0$ Graph

# Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 784c

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
784.e4 784c1 [0, 0, 0, 49, 686] [2] 192 $$\Gamma_0(N)$$-optimal
784.e3 784c2 [0, 0, 0, -931, 10290] [2, 2] 384
784.e2 784c3 [0, 0, 0, -2891, -47334] [2] 768
784.e1 784c4 [0, 0, 0, -14651, 682570] [4] 768

## Rank

sage: E.rank()

The elliptic curves in class 784c have rank $$0$$.

## Complex multiplication

The elliptic curves in class 784c do not have complex multiplication.

## Modular form784.2.a.c

sage: E.q_eigenform(10)

$$q - 2q^{5} - 3q^{9} + 4q^{11} - 2q^{13} + 6q^{17} + 8q^{19} + O(q^{20})$$

## 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 Cremona numbering.

$$\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels.