# Properties

 Label 265200g Number of curves 4 Conductor 265200 CM no Rank 0 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("265200.g1")

sage: E.isogeny_class()

## Elliptic curves in class 265200g

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
265200.g3 265200g1 [0, -1, 0, -1292008, -311097488] [2] 10616832 $$\Gamma_0(N)$$-optimal
265200.g2 265200g2 [0, -1, 0, -9484008, 11026630512] [2, 2] 21233664
265200.g1 265200g3 [0, -1, 0, -150924008, 713700550512] [2] 42467328
265200.g4 265200g4 [0, -1, 0, 883992, 33836230512] [2] 42467328

## Rank

sage: E.rank()

The elliptic curves in class 265200g have rank $$0$$.

## Modular form 265200.2.a.g

sage: E.q_eigenform(10)

$$q - q^{3} - 4q^{7} + q^{9} + 4q^{11} - q^{13} - q^{17} - 8q^{19} + O(q^{20})$$

## 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 Cremona 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 Cremona labels.