# Properties

 Label 274014.q Number of curves 3 Conductor 274014 CM no Rank 1 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("274014.q1")

sage: E.isogeny_class()

## Elliptic curves in class 274014.q

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
274014.q1 274014q3 [1, -1, 1, -34155635, 79795201619]  24074496
274014.q2 274014q1 [1, -1, 1, -320405, -78749395] [] 2674944 $$\Gamma_0(N)$$-optimal
274014.q3 274014q2 [1, -1, 1, 2151220, 292231631]  8024832

## Rank

sage: E.rank()

The elliptic curves in class 274014.q have rank $$1$$.

## Modular form 274014.2.a.q

sage: E.q_eigenform(10)

$$q + q^{2} + q^{4} - q^{7} + q^{8} - 3q^{11} + q^{13} - q^{14} + q^{16} + 3q^{17} + 2q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 