# Properties

 Label 44100.ca Number of curves 4 Conductor 44100 CM no Rank 0 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("44100.ca1")

sage: E.isogeny_class()

## Elliptic curves in class 44100.ca

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
44100.ca1 44100bg3 [0, 0, 0, -455700, -118377875] [2] 311040
44100.ca2 44100bg4 [0, 0, 0, -400575, -148090250] [2] 622080
44100.ca3 44100bg1 [0, 0, 0, -14700, 471625] [2] 103680 $$\Gamma_0(N)$$-optimal
44100.ca4 44100bg2 [0, 0, 0, 40425, 3172750] [2] 207360

## Rank

sage: E.rank()

The elliptic curves in class 44100.ca have rank $$0$$.

## Modular form 44100.2.a.ca

sage: E.q_eigenform(10)

$$q + 2q^{13} + 6q^{17} + 4q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.