Properties

 Label 1440.g Number of curves $4$ Conductor $1440$ CM no Rank $1$ Graph Related objects

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

sage: E.isogeny_class()

Elliptic curves in class 1440.g

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1440.g1 1440g2 $$[0, 0, 0, -32412, -2245984]$$ $$1261112198464/675$$ $$2015539200$$ $$$$ $$3072$$ $$1.1149$$
1440.g2 1440g3 $$[0, 0, 0, -4467, 63974]$$ $$26410345352/10546875$$ $$3936600000000$$ $$$$ $$3072$$ $$1.1149$$
1440.g3 1440g1 $$[0, 0, 0, -2037, -34684]$$ $$20034997696/455625$$ $$21257640000$$ $$[2, 2]$$ $$1536$$ $$0.76837$$ $$\Gamma_0(N)$$-optimal
1440.g4 1440g4 $$[0, 0, 0, 213, -107134]$$ $$2863288/13286025$$ $$-4958982259200$$ $$$$ $$3072$$ $$1.1149$$

Rank

sage: E.rank()

The elliptic curves in class 1440.g have rank $$1$$.

Complex multiplication

The elliptic curves in class 1440.g do not have complex multiplication.

Modular form1440.2.a.g

sage: E.q_eigenform(10)

$$q + q^{5} - 4 q^{7} - 4 q^{11} + 6 q^{13} - 2 q^{17} + 4 q^{19} + O(q^{20})$$ 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 LMFDB numbering.

$$\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)$$

Isogeny graph

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

The vertices are labelled with LMFDB labels. 