# Properties

 Label 265200bo Number of curves $6$ Conductor $265200$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("265200.bo1")

sage: E.isogeny_class()

## Elliptic curves in class 265200bo

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
265200.bo4 265200bo1 [0, -1, 0, -215608, -38462288] [2] 1048576 $$\Gamma_0(N)$$-optimal
265200.bo3 265200bo2 [0, -1, 0, -217608, -37710288] [2, 2] 2097152
265200.bo2 265200bo3 [0, -1, 0, -555608, 108305712] [2, 2] 4194304
265200.bo5 265200bo4 [0, -1, 0, 88392, -135630288] [2] 4194304
265200.bo1 265200bo5 [0, -1, 0, -8069608, 8824545712] [2] 8388608
265200.bo6 265200bo6 [0, -1, 0, 1550392, 731681712] [2] 8388608

## Rank

sage: E.rank()

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

## Modular form 265200.2.a.bo

sage: E.q_eigenform(10)

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

## 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 Cremona numbering.

$$\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 2 & 2 \\ 4 & 2 & 4 & 1 & 8 & 8 \\ 8 & 4 & 2 & 8 & 1 & 4 \\ 8 & 4 & 2 & 8 & 4 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels.