Properties

 Label 4025.f Number of curves $4$ Conductor $4025$ CM no Rank $0$ Graph Related objects

Show commands: SageMath
sage: E = EllipticCurve("f1")

sage: E.isogeny_class()

Elliptic curves in class 4025.f

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4025.f1 4025c4 $$[1, -1, 0, -1052192, 415686091]$$ $$8244966675515989329/3081640625$$ $$48150634765625$$ $$$$ $$34560$$ $$1.9766$$
4025.f2 4025c3 $$[1, -1, 0, -137942, -10015159]$$ $$18577831198352049/7958740140575$$ $$124355314696484375$$ $$$$ $$34560$$ $$1.9766$$
4025.f3 4025c2 $$[1, -1, 0, -66067, 6444216]$$ $$2041085246738049/38897700625$$ $$607776572265625$$ $$[2, 2]$$ $$17280$$ $$1.6301$$
4025.f4 4025c1 $$[1, -1, 0, 58, 294591]$$ $$1367631/2399636575$$ $$-37494321484375$$ $$$$ $$8640$$ $$1.2835$$ $$\Gamma_0(N)$$-optimal

Rank

sage: E.rank()

The elliptic curves in class 4025.f have rank $$0$$.

Complex multiplication

The elliptic curves in class 4025.f do not have complex multiplication.

Modular form4025.2.a.f

sage: E.q_eigenform(10)

$$q + q^{2} - q^{4} + q^{7} - 3 q^{8} - 3 q^{9} - 4 q^{11} + 2 q^{13} + q^{14} - q^{16} - 6 q^{17} - 3 q^{18} + 4 q^{19} + O(q^{20})$$ 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. 