# Properties

 Label 279312.cx Number of curves 2 Conductor 279312 CM no Rank 1 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("279312.cx1")

sage: E.isogeny_class()

## Elliptic curves in class 279312.cx

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
279312.cx1 279312cx2 [0, 1, 0, -10478608, -12957731116] [2] 10813440
279312.cx2 279312cx1 [0, 1, 0, -194848, -481473484] [2] 5406720 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 279312.cx have rank $$1$$.

## Modular form 279312.2.a.cx

sage: E.q_eigenform(10)

$$q + q^{3} - 2q^{7} + q^{9} + q^{11} + 2q^{13} + 2q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.