Properties

 Label 92400g Number of curves $4$ Conductor $92400$ CM no Rank $1$ Graph

Related objects

Show commands: SageMath
sage: E = EllipticCurve("g1")

sage: E.isogeny_class()

Elliptic curves in class 92400g

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
92400.e4 92400g1 $$[0, -1, 0, 1617, -45738]$$ $$1869154304/4611915$$ $$-1152978750000$$ $$[2]$$ $$147456$$ $$0.99831$$ $$\Gamma_0(N)$$-optimal
92400.e3 92400g2 $$[0, -1, 0, -13508, -499488]$$ $$68150496976/12006225$$ $$48024900000000$$ $$[2, 2]$$ $$294912$$ $$1.3449$$
92400.e2 92400g3 $$[0, -1, 0, -63008, 5638512]$$ $$1729010797924/148561875$$ $$2376990000000000$$ $$[2]$$ $$589824$$ $$1.6915$$
92400.e1 92400g4 $$[0, -1, 0, -206008, -35919488]$$ $$60430765429444/2525985$$ $$40415760000000$$ $$[2]$$ $$589824$$ $$1.6915$$

Rank

sage: E.rank()

The elliptic curves in class 92400g have rank $$1$$.

Complex multiplication

The elliptic curves in class 92400g do not have complex multiplication.

Modular form 92400.2.a.g

sage: E.q_eigenform(10)

$$q - q^{3} - q^{7} + q^{9} - q^{11} - 6 q^{13} + 6 q^{17} + 4 q^{19} + O(q^{20})$$

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.