# Properties

 Label 271950bw Number of curves $6$ Conductor $271950$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("271950.bw1")

sage: E.isogeny_class()

## Elliptic curves in class 271950bw

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
271950.bw5 271950bw1 [1, 1, 0, -1035150, -1395895500] [2] 15925248 $$\Gamma_0(N)$$-optimal
271950.bw4 271950bw2 [1, 1, 0, -26123150, -51295927500] [2, 2] 31850496
271950.bw3 271950bw3 [1, 1, 0, -35923150, -9322527500] [2, 2] 63700992
271950.bw1 271950bw4 [1, 1, 0, -417731150, -3286369615500] [2] 63700992
271950.bw2 271950bw5 [1, 1, 0, -371328150, 2742004687500] [2] 127401984
271950.bw6 271950bw6 [1, 1, 0, 142681850, -74156142500] [2] 127401984

## Rank

sage: E.rank()

The elliptic curves in class 271950bw have rank $$0$$.

## Modular form 271950.2.a.bw

sage: E.q_eigenform(10)

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

## 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 Cremona numbering.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels.