Properties

 Label 37440.bl Number of curves $4$ Conductor $37440$ CM no Rank $1$ Graph Related objects

Show commands: SageMath
sage: E = EllipticCurve("bl1")

sage: E.isogeny_class()

Elliptic curves in class 37440.bl

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
37440.bl1 37440bk4 $$[0, 0, 0, -7788, -215152]$$ $$2186875592/428415$$ $$10233922682880$$ $$$$ $$49152$$ $$1.2131$$
37440.bl2 37440bk2 $$[0, 0, 0, -2388, 41888]$$ $$504358336/38025$$ $$113542041600$$ $$[2, 2]$$ $$24576$$ $$0.86651$$
37440.bl3 37440bk1 $$[0, 0, 0, -2343, 43652]$$ $$30488290624/195$$ $$9097920$$ $$$$ $$12288$$ $$0.51993$$ $$\Gamma_0(N)$$-optimal
37440.bl4 37440bk3 $$[0, 0, 0, 2292, 186032]$$ $$55742968/658125$$ $$-15721205760000$$ $$$$ $$49152$$ $$1.2131$$

Rank

sage: E.rank()

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

Complex multiplication

The elliptic curves in class 37440.bl do not have complex multiplication.

Modular form 37440.2.a.bl

sage: E.q_eigenform(10)

$$q - q^{5} + q^{13} - 2 q^{17} - 4 q^{19} + O(q^{20})$$ 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels. 