# Properties

 Label 265200.h Number of curves 4 Conductor 265200 CM no Rank 1 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("265200.h1")

sage: E.isogeny_class()

## Elliptic curves in class 265200.h

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
265200.h1 265200h4 [0, -1, 0, -353608, -80816288] [2] 1572864
265200.h2 265200h3 [0, -1, 0, -28608, -450288] [2] 1572864
265200.h3 265200h2 [0, -1, 0, -22108, -1256288] [2, 2] 786432
265200.h4 265200h1 [0, -1, 0, -983, -31038] [2] 393216 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 265200.h have rank $$1$$.

## Modular form 265200.2.a.h

sage: E.q_eigenform(10)

$$q - q^{3} - 4q^{7} + q^{9} + 4q^{11} - q^{13} - q^{17} + 4q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.