# Properties

 Label 10944.bt Number of curves $2$ Conductor $10944$ CM no Rank $1$ Graph

# Related objects

Show commands: SageMath
E = EllipticCurve("bt1")

E.isogeny_class()

## Elliptic curves in class 10944.bt

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
10944.bt1 10944bt2 $$[0, 0, 0, -158052, -24185162]$$ $$-9358714467168256/22284891$$ $$-1039723874496$$ $$[]$$ $$38400$$ $$1.5473$$
10944.bt2 10944bt1 $$[0, 0, 0, 708, -8282]$$ $$841232384/1121931$$ $$-52344812736$$ $$[]$$ $$7680$$ $$0.74257$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 10944.bt have rank $$1$$.

## Complex multiplication

The elliptic curves in class 10944.bt do not have complex multiplication.

## Modular form10944.2.a.bt

sage: E.q_eigenform(10)

$$q + q^{5} - 3 q^{7} + 3 q^{11} + 6 q^{13} - 3 q^{17} - q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.