Properties

 Label 29400cp Number of curves $4$ Conductor $29400$ CM no Rank $1$ Graph

Related objects

Show commands for: SageMath
sage: E = EllipticCurve("cp1")

sage: E.isogeny_class()

Elliptic curves in class 29400cp

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
29400.bb4 29400cp1 [0, -1, 0, 10617, 3472512] [2] 147456 $$\Gamma_0(N)$$-optimal
29400.bb3 29400cp2 [0, -1, 0, -289508, 57495012] [2, 2] 294912
29400.bb2 29400cp3 [0, -1, 0, -804008, -202841988] [2] 589824
29400.bb1 29400cp4 [0, -1, 0, -4577008, 3770470012] [2] 589824

Rank

sage: E.rank()

The elliptic curves in class 29400cp have rank $$1$$.

Complex multiplication

The elliptic curves in class 29400cp do not have complex multiplication.

Modular form 29400.2.a.cp

sage: E.q_eigenform(10)

$$q - q^{3} + q^{9} - 2q^{13} + 6q^{17} + 4q^{19} + O(q^{20})$$

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 Cremona numbering.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.