Properties

 Label 5520.g Number of curves $2$ Conductor $5520$ CM no Rank $1$ Graph

Related objects

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

sage: E.isogeny_class()

Elliptic curves in class 5520.g

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
5520.g1 5520o2 $$[0, -1, 0, -1381, 20425]$$ $$-1138621087744/13687875$$ $$-3504096000$$ $$[]$$ $$3456$$ $$0.64321$$
5520.g2 5520o1 $$[0, -1, 0, 59, 121]$$ $$87228416/83835$$ $$-21461760$$ $$[]$$ $$1152$$ $$0.093906$$ $$\Gamma_0(N)$$-optimal

Rank

sage: E.rank()

The elliptic curves in class 5520.g have rank $$1$$.

Complex multiplication

The elliptic curves in class 5520.g do not have complex multiplication.

Modular form5520.2.a.g

sage: E.q_eigenform(10)

$$q - q^{3} - q^{5} + q^{7} + q^{9} - 4 q^{13} + q^{15} - 3 q^{17} + 4 q^{19} + O(q^{20})$$

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.

$$\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)$$

Isogeny graph

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

The vertices are labelled with LMFDB labels.