Properties

 Label 38640.cf Number of curves $4$ Conductor $38640$ CM no Rank $0$ Graph

Related objects

Show commands: SageMath
sage: E = EllipticCurve("cf1")

sage: E.isogeny_class()

Elliptic curves in class 38640.cf

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
38640.cf1 38640cn4 $$[0, 1, 0, -71856, 7389780]$$ $$10017490085065009/235066440$$ $$962832138240$$ $$[2]$$ $$147456$$ $$1.4114$$
38640.cf2 38640cn3 $$[0, 1, 0, -19376, -936876]$$ $$196416765680689/22365315000$$ $$91608330240000$$ $$[2]$$ $$147456$$ $$1.4114$$
38640.cf3 38640cn2 $$[0, 1, 0, -4656, 105300]$$ $$2725812332209/373262400$$ $$1528882790400$$ $$[2, 2]$$ $$73728$$ $$1.0649$$
38640.cf4 38640cn1 $$[0, 1, 0, 464, 9044]$$ $$2691419471/9891840$$ $$-40516976640$$ $$[2]$$ $$36864$$ $$0.71829$$ $$\Gamma_0(N)$$-optimal

Rank

sage: E.rank()

The elliptic curves in class 38640.cf have rank $$0$$.

Complex multiplication

The elliptic curves in class 38640.cf do not have complex multiplication.

Modular form 38640.2.a.cf

sage: E.q_eigenform(10)

$$q + q^{3} - q^{5} - q^{7} + q^{9} + 4q^{11} - 2q^{13} - q^{15} + 6q^{17} + 4q^{19} + O(q^{20})$$

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.