Properties

 Label 7406.c Number of curves $2$ Conductor $7406$ CM no Rank $1$ Graph Related objects

Show commands: SageMath
sage: E = EllipticCurve("c1")

sage: E.isogeny_class()

Elliptic curves in class 7406.c

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
7406.c1 7406e2 $$[1, -1, 0, -467, -3735]$$ $$926859375/9604$$ $$116851868$$ $$$$ $$2304$$ $$0.36507$$
7406.c2 7406e1 $$[1, -1, 0, -7, -147]$$ $$-3375/784$$ $$-9538928$$ $$$$ $$1152$$ $$0.018494$$ $$\Gamma_0(N)$$-optimal

Rank

sage: E.rank()

The elliptic curves in class 7406.c have rank $$1$$.

Complex multiplication

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

Modular form7406.2.a.c

sage: E.q_eigenform(10)

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels. 