Properties

 Label 271440cd Number of curves $4$ Conductor $271440$ CM no Rank $0$ Graph Related objects

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

sage: E.isogeny_class()

Elliptic curves in class 271440cd

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
271440.cd3 271440cd1 $$[0, 0, 0, -255243, 49632442]$$ $$615882348586441/21715200$$ $$64841239756800$$ $$$$ $$2359296$$ $$1.7400$$ $$\Gamma_0(N)$$-optimal
271440.cd2 271440cd2 $$[0, 0, 0, -266763, 44906938]$$ $$703093388853961/115124490000$$ $$343759885148160000$$ $$[2, 2]$$ $$4718592$$ $$2.0866$$
271440.cd4 271440cd3 $$[0, 0, 0, 484917, 252220282]$$ $$4223169036960119/11647532812500$$ $$-34779346617600000000$$ $$$$ $$9437184$$ $$2.4332$$
271440.cd1 271440cd4 $$[0, 0, 0, -1202763, -464838662]$$ $$64443098670429961/6032611833300$$ $$18013282412444467200$$ $$$$ $$9437184$$ $$2.4332$$

Rank

sage: E.rank()

The elliptic curves in class 271440cd have rank $$0$$.

Complex multiplication

The elliptic curves in class 271440cd do not have complex multiplication.

Modular form 271440.2.a.cd

sage: E.q_eigenform(10)

$$q - q^{5} + 4 q^{7} - 4 q^{11} + q^{13} + 6 q^{17} + 4 q^{19} + O(q^{20})$$ 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. 