# Properties

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

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("265200.j1")

sage: E.isogeny_class()

## Elliptic curves in class 265200.j

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
265200.j1 265200j3 [0, -1, 0, -559408, 155509312] [2] 4718592
265200.j2 265200j2 [0, -1, 0, -91408, -7354688] [2, 2] 2359296
265200.j3 265200j1 [0, -1, 0, -83408, -9242688] [2] 1179648 $$\Gamma_0(N)$$-optimal
265200.j4 265200j4 [0, -1, 0, 248592, -49514688] [2] 4718592

## Rank

sage: E.rank()

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

## Modular form 265200.2.a.j

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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.