# Properties

 Label 2541b Number of curves 6 Conductor 2541 CM no Rank 0 Graph

# Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("2541.h1")

sage: E.isogeny_class()

## Elliptic curves in class 2541b

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
2541.h4 2541b1 [1, 1, 0, -4116, -103341] [2] 2400 $$\Gamma_0(N)$$-optimal
2541.h3 2541b2 [1, 1, 0, -4721, -71760] [2, 2] 4800
2541.h2 2541b3 [1, 1, 0, -34366, 2388775] [2, 2] 9600
2541.h6 2541b4 [1, 1, 0, 15244, -499011] [2] 9600
2541.h1 2541b5 [1, 1, 0, -546801, 155401866] [2] 19200
2541.h5 2541b6 [1, 1, 0, 3749, 7442824] [2] 19200

## Rank

sage: E.rank()

The elliptic curves in class 2541b have rank $$0$$.

## Modular form2541.2.a.h

sage: E.q_eigenform(10)

$$q + q^{2} - q^{3} - q^{4} - 2q^{5} - q^{6} - q^{7} - 3q^{8} + q^{9} - 2q^{10} + q^{12} - 6q^{13} - q^{14} + 2q^{15} - q^{16} - 2q^{17} + q^{18} - 4q^{19} + O(q^{20})$$

## 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.