Properties

 Label 372810n Number of curves $4$ Conductor $372810$ CM no Rank $2$ Graph

Related objects

Show commands for: SageMath
sage: E = EllipticCurve("n1")

sage: E.isogeny_class()

Elliptic curves in class 372810n

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
372810.n3 372810n1 [1, 1, 0, -19802, -1079484] [2] 983040 $$\Gamma_0(N)$$-optimal
372810.n2 372810n2 [1, 1, 0, -25582, -405536] [2, 2] 1966080
372810.n1 372810n3 [1, 1, 0, -242332, 45502114] [2] 3932160
372810.n4 372810n4 [1, 1, 0, 98688, -3064914] [2] 3932160

Rank

sage: E.rank()

The elliptic curves in class 372810n have rank $$2$$.

Complex multiplication

The elliptic curves in class 372810n do not have complex multiplication.

Modular form 372810.2.a.n

sage: E.q_eigenform(10)

$$q - q^{2} - q^{3} + q^{4} + q^{5} + q^{6} - 4q^{7} - q^{8} + q^{9} - q^{10} - q^{12} - 2q^{13} + 4q^{14} - q^{15} + q^{16} - q^{18} + 4q^{19} + O(q^{20})$$

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 Cremona numbering.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.