# Properties

 Label 148225cp Number of curves $2$ Conductor $148225$ CM no Rank $1$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("cp1")

sage: E.isogeny_class()

## Elliptic curves in class 148225cp

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
148225.co2 148225cp1 [1, 1, 0, -36775, 2699250] [] 302400 $$\Gamma_0(N)$$-optimal
148225.co1 148225cp2 [1, 1, 0, -373650, -343810375] [] 3326400

## Rank

sage: E.rank()

The elliptic curves in class 148225cp have rank $$1$$.

## Complex multiplication

The elliptic curves in class 148225cp do not have complex multiplication.

## Modular form 148225.2.a.cp

sage: E.q_eigenform(10)

$$q + q^{2} + 2q^{3} - q^{4} + 2q^{6} - 3q^{8} + q^{9} - 2q^{12} - q^{13} - q^{16} + 5q^{17} + q^{18} + 6q^{19} + O(q^{20})$$

## 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 Cremona numbering.

$$\left(\begin{array}{rr} 1 & 11 \\ 11 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels. 