# Properties

 Label 121275dp Number of curves $2$ Conductor $121275$ CM no Rank $1$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("dp1")

sage: E.isogeny_class()

## Elliptic curves in class 121275dp

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
121275.a2 121275dp1 [0, 0, 1, -98567175, 441097174656] [] 55296000 $$\Gamma_0(N)$$-optimal
121275.a1 121275dp2 [0, 0, 1, -295363425, -36938069991594] [] 276480000

## Rank

sage: E.rank()

The elliptic curves in class 121275dp have rank $$1$$.

## Complex multiplication

The elliptic curves in class 121275dp do not have complex multiplication.

## Modular form 121275.2.a.dp

sage: E.q_eigenform(10)

$$q - 2q^{2} + 2q^{4} - q^{11} - 6q^{13} - 4q^{16} + 7q^{17} + 5q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels.