# Properties

 Label 3179c Number of curves 3 Conductor 3179 CM no Rank 1 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("3179.a1")

sage: E.isogeny_class()

## Elliptic curves in class 3179c

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
3179.a3 3179c1 [0, 1, 1, -96, 832] [] 1024 $$\Gamma_0(N)$$-optimal
3179.a2 3179c2 [0, 1, 1, -2986, -114768] [] 5120
3179.a1 3179c3 [0, 1, 1, -2260076, -1308527588] [] 25600

## Rank

sage: E.rank()

The elliptic curves in class 3179c have rank $$1$$.

## Modular form3179.2.a.a

sage: E.q_eigenform(10)

$$q - 2q^{2} + q^{3} + 2q^{4} - q^{5} - 2q^{6} + 2q^{7} - 2q^{9} + 2q^{10} - q^{11} + 2q^{12} + 4q^{13} - 4q^{14} - q^{15} - 4q^{16} + 4q^{18} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrr} 1 & 5 & 25 \\ 5 & 1 & 5 \\ 25 & 5 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels.