Properties

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

Related objects

Show commands: SageMath
E = EllipticCurve("o1")

E.isogeny_class()

Elliptic curves in class 3192.o

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3192.o1 3192h2 $$[0, 1, 0, -628, 5456]$$ $$107165266000/7853517$$ $$2010500352$$ $$[2]$$ $$1280$$ $$0.53127$$
3192.o2 3192h1 $$[0, 1, 0, 37, 402]$$ $$340736000/4298427$$ $$-68774832$$ $$[2]$$ $$640$$ $$0.18470$$ $$\Gamma_0(N)$$-optimal

Rank

sage: E.rank()

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

Complex multiplication

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

Modular form3192.2.a.o

sage: E.q_eigenform(10)

$$q + q^{3} + q^{7} + q^{9} - 2 q^{13} - 8 q^{17} - q^{19} + O(q^{20})$$

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.