# Properties

 Label 279312bp Number of curves 4 Conductor 279312 CM no Rank 0 Graph

# Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("279312.bp1")

sage: E.isogeny_class()

## Elliptic curves in class 279312bp

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
279312.bp4 279312bp1 [0, -1, 0, 353, 69730] [2] 608256 $$\Gamma_0(N)$$-optimal
279312.bp3 279312bp2 [0, -1, 0, -23452, 1355200] [2, 2] 1216512
279312.bp1 279312bp3 [0, -1, 0, -372592, 87662608] [2] 2433024
279312.bp2 279312bp4 [0, -1, 0, -55192, -3063008] [2] 2433024

## Rank

sage: E.rank()

The elliptic curves in class 279312bp have rank $$0$$.

## Modular form 279312.2.a.bp

sage: E.q_eigenform(10)

$$q - q^{3} + 2q^{5} + 4q^{7} + q^{9} - q^{11} + 6q^{13} - 2q^{15} - 6q^{17} - 8q^{19} + O(q^{20})$$

## 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.