Properties

 Label 37440.eq Number of curves $6$ Conductor $37440$ CM no Rank $1$ Graph

Related objects

Show commands for: SageMath
sage: E = EllipticCurve("37440.eq1")

sage: E.isogeny_class()

Elliptic curves in class 37440.eq

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
37440.eq1 37440cb6 [0, 0, 0, -5192652, 4554407536] [2] 786432
37440.eq2 37440cb4 [0, 0, 0, -486732, -130599056] [2] 393216
37440.eq3 37440cb3 [0, 0, 0, -325452, 70742896] [2, 2] 393216
37440.eq4 37440cb5 [0, 0, 0, -66252, 180332656] [2] 786432
37440.eq5 37440cb2 [0, 0, 0, -37452, -1026704] [2, 2] 196608
37440.eq6 37440cb1 [0, 0, 0, 8628, -123536] [2] 98304 $$\Gamma_0(N)$$-optimal

Rank

sage: E.rank()

The elliptic curves in class 37440.eq have rank $$1$$.

Modular form 37440.2.a.eq

sage: E.q_eigenform(10)

$$q + q^{5} + 4q^{11} - q^{13} + 6q^{17} - 4q^{19} + O(q^{20})$$

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 LMFDB numbering.

$$\left(\begin{array}{rrrrrr} 1 & 8 & 2 & 4 & 4 & 8 \\ 8 & 1 & 4 & 8 & 2 & 4 \\ 2 & 4 & 1 & 2 & 2 & 4 \\ 4 & 8 & 2 & 1 & 4 & 8 \\ 4 & 2 & 2 & 4 & 1 & 2 \\ 8 & 4 & 4 & 8 & 2 & 1 \end{array}\right)$$

Isogeny graph

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

The vertices are labelled with LMFDB labels.