# Properties

 Label 101150c Number of curves $4$ Conductor $101150$ CM no Rank $1$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("101150.o1")

sage: E.isogeny_class()

## Elliptic curves in class 101150c

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
101150.o4 101150c1 [1, -1, 0, 16708, -1328384]  491520 $$\Gamma_0(N)$$-optimal
101150.o3 101150c2 [1, -1, 0, -127792, -14188884] [2, 2] 983040
101150.o2 101150c3 [1, -1, 0, -633542, 181536366]  1966080
101150.o1 101150c4 [1, -1, 0, -1934042, -1034720134]  1966080

## Rank

sage: E.rank()

The elliptic curves in class 101150c have rank $$1$$.

## Modular form 101150.2.a.o

sage: E.q_eigenform(10)

$$q - q^{2} + q^{4} - q^{7} - q^{8} - 3q^{9} - 4q^{11} + 6q^{13} + q^{14} + q^{16} + 3q^{18} + O(q^{20})$$

## 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. 