# Properties

 Label 124950.cb Number of curves $6$ Conductor $124950$ CM no Rank $1$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("124950.cb1")

sage: E.isogeny_class()

## Elliptic curves in class 124950.cb

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
124950.cb1 124950ba6 [1, 1, 0, -16805289925, 838520099849125]  188743680
124950.cb2 124950ba4 [1, 1, 0, -1052328925, 13049190488125] [2, 2] 94371840
124950.cb3 124950ba5 [1, 1, 0, -358439925, 30001592647125]  188743680
124950.cb4 124950ba2 [1, 1, 0, -111136925, -113379631875] [2, 2] 47185920
124950.cb5 124950ba1 [1, 1, 0, -86048925, -306883375875]  23592960 $$\Gamma_0(N)$$-optimal
124950.cb6 124950ba3 [1, 1, 0, 428647075, -891208375875]  94371840

## Rank

sage: E.rank()

The elliptic curves in class 124950.cb have rank $$1$$.

## Modular form 124950.2.a.cb

sage: E.q_eigenform(10)

$$q - q^{2} - q^{3} + q^{4} + q^{6} - q^{8} + q^{9} + 4q^{11} - q^{12} - 2q^{13} + q^{16} + q^{17} - q^{18} - 4q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 