# Properties

 Label 127050cv Number of curves $4$ Conductor $127050$ CM no Rank $1$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("cv1")

sage: E.isogeny_class()

## Elliptic curves in class 127050cv

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
127050.cr3 127050cv1 [1, 0, 1, -10651, 266198]  491520 $$\Gamma_0(N)$$-optimal
127050.cr2 127050cv2 [1, 0, 1, -71151, -7114802] [2, 2] 983040
127050.cr4 127050cv3 [1, 0, 1, 19599, -23994302]  1966080
127050.cr1 127050cv4 [1, 0, 1, -1129901, -462377302]  1966080

## Rank

sage: E.rank()

The elliptic curves in class 127050cv have rank $$1$$.

## Complex multiplication

The elliptic curves in class 127050cv do not have complex multiplication.

## Modular form 127050.2.a.cv

sage: E.q_eigenform(10)

$$q - q^{2} + q^{3} + q^{4} - q^{6} - q^{7} - q^{8} + q^{9} + q^{12} - 2q^{13} + q^{14} + q^{16} - 6q^{17} - q^{18} + O(q^{20})$$

## 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. 