# Properties

 Label 2925.k Number of curves $2$ Conductor $2925$ CM no Rank $1$ Graph

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("k1")

sage: E.isogeny_class()

## Elliptic curves in class 2925.k

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2925.k1 2925a2 $$[0, 0, 1, -9450, -355219]$$ $$-303464448/1625$$ $$-499763671875$$ $$[]$$ $$3456$$ $$1.0893$$
2925.k2 2925a1 $$[0, 0, 1, 300, -2594]$$ $$7077888/10985$$ $$-4634296875$$ $$[]$$ $$1152$$ $$0.54000$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 2925.k have rank $$1$$.

## Complex multiplication

The elliptic curves in class 2925.k do not have complex multiplication.

## Modular form2925.2.a.k

sage: E.q_eigenform(10)

$$q - 2 q^{4} + q^{7} + 3 q^{11} - q^{13} + 4 q^{16} - 3 q^{17} - 4 q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.