Properties

 Label 3192.e Number of curves $2$ Conductor $3192$ CM no Rank $1$ Graph

Related objects

Show commands: SageMath
E = EllipticCurve("e1")

E.isogeny_class()

Elliptic curves in class 3192.e

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3192.e1 3192k1 $$[0, -1, 0, -43, 124]$$ $$562432000/1197$$ $$19152$$ $$[2]$$ $$256$$ $$-0.29376$$ $$\Gamma_0(N)$$-optimal
3192.e2 3192k2 $$[0, -1, 0, -28, 196]$$ $$-9826000/53067$$ $$-13585152$$ $$[2]$$ $$512$$ $$0.052814$$

Rank

sage: E.rank()

The elliptic curves in class 3192.e have rank $$1$$.

Complex multiplication

The elliptic curves in class 3192.e do not have complex multiplication.

Modular form3192.2.a.e

sage: E.q_eigenform(10)

$$q - q^{3} - q^{7} + q^{9} - 2 q^{13} + q^{19} + O(q^{20})$$

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 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.