# Properties

 Label 126852c Number of curves 2 Conductor 126852 CM no Rank 1 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("126852.e1")

sage: E.isogeny_class()

## Elliptic curves in class 126852c

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
126852.e2 126852c1 [0, -1, 0, 2563, 26730] [2] 172800 $$\Gamma_0(N)$$-optimal
126852.e1 126852c2 [0, -1, 0, -11852, 240072] [2] 345600

## Rank

sage: E.rank()

The elliptic curves in class 126852c have rank $$1$$.

## Modular form 126852.2.a.e

sage: E.q_eigenform(10)

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

## 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.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels.