Properties

 Label 123840cd Number of curves $4$ Conductor $123840$ CM no Rank $1$ Graph

Related objects

Show commands for: SageMath
sage: E = EllipticCurve("cd1")

sage: E.isogeny_class()

Elliptic curves in class 123840cd

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
123840.dk3 123840cd1 [0, 0, 0, -39468, 3014192] [2] 294912 $$\Gamma_0(N)$$-optimal
123840.dk2 123840cd2 [0, 0, 0, -50988, 1111088] [2, 2] 589824
123840.dk4 123840cd3 [0, 0, 0, 196692, 8739632] [2] 1179648
123840.dk1 123840cd4 [0, 0, 0, -482988, -128316112] [2] 1179648

Rank

sage: E.rank()

The elliptic curves in class 123840cd have rank $$1$$.

Complex multiplication

The elliptic curves in class 123840cd do not have complex multiplication.

Modular form 123840.2.a.cd

sage: E.q_eigenform(10)

$$q - q^{5} + 4q^{7} + 2q^{13} - 2q^{17} - 4q^{19} + O(q^{20})$$

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.