Properties

 Label 7406.d Number of curves $2$ Conductor $7406$ CM no Rank $0$ Graph Related objects

Show commands: SageMath
sage: E = EllipticCurve("d1")

sage: E.isogeny_class()

Elliptic curves in class 7406.d

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
7406.d1 7406b2 $$[1, -1, 0, -126001, -17129673]$$ $$1494447319737/5411854$$ $$801148618028206$$ $$$$ $$50688$$ $$1.7208$$
7406.d2 7406b1 $$[1, -1, 0, -4331, -509551]$$ $$-60698457/725788$$ $$-107442671805532$$ $$$$ $$25344$$ $$1.3742$$ $$\Gamma_0(N)$$-optimal

Rank

sage: E.rank()

The elliptic curves in class 7406.d have rank $$0$$.

Complex multiplication

The elliptic curves in class 7406.d do not have complex multiplication.

Modular form7406.2.a.d

sage: E.q_eigenform(10)

$$q - q^{2} + q^{4} + 2 q^{5} - q^{7} - q^{8} - 3 q^{9} - 2 q^{10} + 4 q^{11} + 4 q^{13} + q^{14} + q^{16} + 8 q^{17} + 3 q^{18} + 2 q^{19} + O(q^{20})$$ 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. 