# Properties

 Label 25872cp Number of curves 2 Conductor 25872 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("25872.bs1")

sage: E.isogeny_class()

## Elliptic curves in class 25872cp

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
25872.bs2 25872cp1 [0, 1, 0, 131, -274]  8640 $$\Gamma_0(N)$$-optimal
25872.bs1 25872cp2 [0, 1, 0, -604, -2920]  17280

## Rank

sage: E.rank()

The elliptic curves in class 25872cp have rank $$0$$.

## Modular form 25872.2.a.bs

sage: E.q_eigenform(10)

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

## 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. 