# Properties

 Label 3025.b Number of curves $2$ Conductor $3025$ CM no Rank $0$ Graph

# Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 3025.b

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
3025.b1 3025e2 [1, 0, 0, -90813, 10526242] [] 9240
3025.b2 3025e1 [1, 0, 0, -63, -758] [] 840 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 3025.b have rank $$0$$.

## Complex multiplication

The elliptic curves in class 3025.b do not have complex multiplication.

## Modular form3025.2.a.b

sage: E.q_eigenform(10)

$$q - q^{2} - 2q^{3} - q^{4} + 2q^{6} + 2q^{7} + 3q^{8} + q^{9} + 2q^{12} - q^{13} - 2q^{14} - q^{16} + 5q^{17} - q^{18} + 6q^{19} + O(q^{20})$$

## 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 LMFDB 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 LMFDB labels.