# Properties

 Label 525.b Number of curves $2$ Conductor $525$ CM no Rank $1$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("525.b1")

sage: E.isogeny_class()

## Elliptic curves in class 525.b

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
525.b1 525d1 [1, 0, 0, -18, 27]  48 $$\Gamma_0(N)$$-optimal
525.b2 525d2 [1, 0, 0, 7, 102]  96

## Rank

sage: E.rank()

The elliptic curves in class 525.b have rank $$1$$.

## Modular form525.2.a.b

sage: E.q_eigenform(10)

$$q - q^{2} + q^{3} - q^{4} - q^{6} - q^{7} + 3q^{8} + q^{9} - 6q^{11} - q^{12} - 2q^{13} + q^{14} - q^{16} + 4q^{17} - q^{18} - 6q^{19} + O(q^{20})$$

## 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 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. 