# Properties

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

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("265200.i1")

sage: E.isogeny_class()

## Elliptic curves in class 265200.i

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
265200.i1 265200i3 [0, -1, 0, -418408, 104299312] [2] 2752512
265200.i2 265200i2 [0, -1, 0, -28408, 1339312] [2, 2] 1376256
265200.i3 265200i1 [0, -1, 0, -10408, -388688] [2] 688128 $$\Gamma_0(N)$$-optimal
265200.i4 265200i4 [0, -1, 0, 73592, 8683312] [2] 2752512

## Rank

sage: E.rank()

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

## Modular form 265200.2.a.i

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.