# Properties

 Label 25410.h Number of curves 4 Conductor 25410 CM no Rank 1 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("25410.h1")

sage: E.isogeny_class()

## Elliptic curves in class 25410.h

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
25410.h1 25410h4 [1, 1, 0, -3991913, -3071494257] [2] 737280
25410.h2 25410h2 [1, 1, 0, -256643, -45178503] [2, 2] 368640
25410.h3 25410h1 [1, 1, 0, -60623, 4963413] [2] 184320 $$\Gamma_0(N)$$-optimal
25410.h4 25410h3 [1, 1, 0, 342307, -224024973] [2] 737280

## Rank

sage: E.rank()

The elliptic curves in class 25410.h have rank $$1$$.

## Modular form 25410.2.a.h

sage: E.q_eigenform(10)

$$q - q^{2} - q^{3} + q^{4} - q^{5} + q^{6} + q^{7} - q^{8} + q^{9} + q^{10} - q^{12} - 2q^{13} - q^{14} + q^{15} + q^{16} - 2q^{17} - q^{18} - 4q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.