Properties

 Label 397800.cg Number of curves $2$ Conductor $397800$ CM no Rank $0$ Graph

Related objects

Show commands: SageMath
sage: E = EllipticCurve("cg1")

sage: E.isogeny_class()

Elliptic curves in class 397800.cg

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
397800.cg1 397800cg1 $$[0, 0, 0, -63228675, -193227039250]$$ $$2396726313900986596/4154072495625$$ $$48453101588970000000000$$ $$[2]$$ $$35389440$$ $$3.2468$$ $$\Gamma_0(N)$$-optimal
397800.cg2 397800cg2 $$[0, 0, 0, -43455675, -316274418250]$$ $$-389032340685029858/1627263833203125$$ $$-37960810700962500000000000$$ $$[2]$$ $$70778880$$ $$3.5934$$

Rank

sage: E.rank()

The elliptic curves in class 397800.cg have rank $$0$$.

Complex multiplication

The elliptic curves in class 397800.cg do not have complex multiplication.

Modular form 397800.2.a.cg

sage: E.q_eigenform(10)

$$q - 2 q^{11} + q^{13} - q^{17} - 8 q^{19} + O(q^{20})$$

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.