Properties

 Label 243360bj Number of curves $4$ Conductor $243360$ CM no Rank $1$ Graph Related objects

Show commands: SageMath
sage: E = EllipticCurve("bj1")

sage: E.isogeny_class()

Elliptic curves in class 243360bj

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
243360.bj3 243360bj1 $$[0, 0, 0, -100893, 11503492]$$ $$504358336/38025$$ $$8563214816769600$$ $$[2, 2]$$ $$1032192$$ $$1.8024$$ $$\Gamma_0(N)$$-optimal
243360.bj1 243360bj2 $$[0, 0, 0, -1583868, 767227552]$$ $$30488290624/195$$ $$2810491016785920$$ $$$$ $$2064384$$ $$2.1490$$
243360.bj4 243360bj3 $$[0, 0, 0, 96837, 51089038]$$ $$55742968/658125$$ $$-1185675897706560000$$ $$$$ $$2064384$$ $$2.1490$$
243360.bj2 243360bj4 $$[0, 0, 0, -329043, -59086118]$$ $$2186875592/428415$$ $$771831095484833280$$ $$$$ $$2064384$$ $$2.1490$$

Rank

sage: E.rank()

The elliptic curves in class 243360bj have rank $$1$$.

Complex multiplication

The elliptic curves in class 243360bj do not have complex multiplication.

Modular form 243360.2.a.bj

sage: E.q_eigenform(10)

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

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

Isogeny graph

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

The vertices are labelled with Cremona labels. 