Properties

 Label 1152.l Number of curves $2$ Conductor $1152$ CM no Rank $0$ Graph Related objects

Show commands: SageMath
sage: E = EllipticCurve("l1")

sage: E.isogeny_class()

Elliptic curves in class 1152.l

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1152.l1 1152e2 $$[0, 0, 0, -120, 416]$$ $$16000/3$$ $$35831808$$ $$$$ $$256$$ $$0.16743$$
1152.l2 1152e1 $$[0, 0, 0, 15, 38]$$ $$4000/9$$ $$-839808$$ $$$$ $$128$$ $$-0.17914$$ $$\Gamma_0(N)$$-optimal

Rank

sage: E.rank()

The elliptic curves in class 1152.l have rank $$0$$.

Complex multiplication

The elliptic curves in class 1152.l do not have complex multiplication.

Modular form1152.2.a.l

sage: E.q_eigenform(10)

$$q + 2 q^{7} + 4 q^{11} + 6 q^{13} - 6 q^{17} + O(q^{20})$$ 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. 