Properties

 Label 271440.v Number of curves $2$ Conductor $271440$ CM no Rank $0$ Graph Related objects

Show commands: SageMath
sage: E = EllipticCurve("v1")

sage: E.isogeny_class()

Elliptic curves in class 271440.v

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
271440.v1 271440v1 $$[0, 0, 0, -119883, 13591802]$$ $$63812982460681/10201800960$$ $$30462414437744640$$ $$$$ $$1474560$$ $$1.8853$$ $$\Gamma_0(N)$$-optimal
271440.v2 271440v2 $$[0, 0, 0, 214197, 75797498]$$ $$363979050334199/1041836936400$$ $$-3110908422699417600$$ $$$$ $$2949120$$ $$2.2319$$

Rank

sage: E.rank()

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

Complex multiplication

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

Modular form 271440.2.a.v

sage: E.q_eigenform(10)

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels. 