Properties

 Label 224400.co Number of curves 6 Conductor 224400 CM no Rank 1 Graph

Related objects

Show commands for: SageMath
sage: E = EllipticCurve("224400.co1")

sage: E.isogeny_class()

Elliptic curves in class 224400.co

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
224400.co1 224400fd5 [0, -1, 0, -116856008, 486191974512] [2] 28311552
224400.co2 224400fd3 [0, -1, 0, -7956008, 6160774512] [2, 2] 14155776
224400.co3 224400fd2 [0, -1, 0, -2956008, -1879225488] [2, 2] 7077888
224400.co4 224400fd1 [0, -1, 0, -2924008, -1923513488] [2] 3538944 $$\Gamma_0(N)$$-optimal
224400.co5 224400fd4 [0, -1, 0, 1531992, -7085305488] [2] 14155776
224400.co6 224400fd6 [0, -1, 0, 20943992, 40609574512] [2] 28311552

Rank

sage: E.rank()

The elliptic curves in class 224400.co have rank $$1$$.

Modular form 224400.2.a.co

sage: E.q_eigenform(10)

$$q - q^{3} + q^{9} + q^{11} - 6q^{13} - q^{17} - 4q^{19} + O(q^{20})$$

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.