Properties

 Label 93600.cp Number of curves $4$ Conductor $93600$ CM no Rank $0$ Graph Related objects

Show commands: SageMath
sage: E = EllipticCurve("cp1")

sage: E.isogeny_class()

Elliptic curves in class 93600.cp

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
93600.cp1 93600dt4 $$[0, 0, 0, -234300, 43652000]$$ $$30488290624/195$$ $$9097920000000$$ $$$$ $$294912$$ $$1.6712$$
93600.cp2 93600dt3 $$[0, 0, 0, -48675, -3361750]$$ $$2186875592/428415$$ $$2498516280000000$$ $$$$ $$294912$$ $$1.6712$$
93600.cp3 93600dt1 $$[0, 0, 0, -14925, 654500]$$ $$504358336/38025$$ $$27720225000000$$ $$[2, 2]$$ $$147456$$ $$1.3247$$ $$\Gamma_0(N)$$-optimal
93600.cp4 93600dt2 $$[0, 0, 0, 14325, 2906750]$$ $$55742968/658125$$ $$-3838185000000000$$ $$$$ $$294912$$ $$1.6712$$

Rank

sage: E.rank()

The elliptic curves in class 93600.cp have rank $$0$$.

Complex multiplication

The elliptic curves in class 93600.cp do not have complex multiplication.

Modular form 93600.2.a.cp

sage: E.q_eigenform(10)

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels. 