Properties

 Label 265200.fi Number of curves $4$ Conductor $265200$ CM no Rank $0$ Graph

Related objects

Show commands: SageMath
sage: E = EllipticCurve("fi1")

sage: E.isogeny_class()

Elliptic curves in class 265200.fi

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
265200.fi1 265200fi3 $$[0, 1, 0, -1562408, 751165188]$$ $$26362547147244676/244298925$$ $$3908782800000000$$ $$[2]$$ $$3538944$$ $$2.1555$$
265200.fi2 265200fi2 $$[0, 1, 0, -99908, 11140188]$$ $$27572037674704/2472575625$$ $$9890302500000000$$ $$[2, 2]$$ $$1769472$$ $$1.8089$$
265200.fi3 265200fi1 $$[0, 1, 0, -21783, -1047312]$$ $$4572531595264/776953125$$ $$194238281250000$$ $$[2]$$ $$884736$$ $$1.4623$$ $$\Gamma_0(N)$$-optimal
265200.fi4 265200fi4 $$[0, 1, 0, 112592, 52365188]$$ $$9865576607324/79640206425$$ $$-1274243302800000000$$ $$[2]$$ $$3538944$$ $$2.1555$$

Rank

sage: E.rank()

The elliptic curves in class 265200.fi have rank $$0$$.

Complex multiplication

The elliptic curves in class 265200.fi do not have complex multiplication.

Modular form 265200.2.a.fi

sage: E.q_eigenform(10)

$$q + q^{3} + q^{9} - 4 q^{11} - q^{13} - q^{17} + 8 q^{19} + O(q^{20})$$

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.