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SageMath
E = EllipticCurve("ge1")
E.isogeny_class()
Elliptic curves in class 148800.ge
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
148800.ge1 | 148800hc4 | \([0, 1, 0, -2421633, -1388815137]\) | \(383432500775449/18701300250\) | \(76600525824000000000\) | \([2]\) | \(5308416\) | \(2.5750\) | |
148800.ge2 | 148800hc2 | \([0, 1, 0, -421633, 77184863]\) | \(2023804595449/540562500\) | \(2214144000000000000\) | \([2, 2]\) | \(2654208\) | \(2.2285\) | |
148800.ge3 | 148800hc1 | \([0, 1, 0, -389633, 93472863]\) | \(1597099875769/186000\) | \(761856000000000\) | \([2]\) | \(1327104\) | \(1.8819\) | \(\Gamma_0(N)\)-optimal |
148800.ge4 | 148800hc3 | \([0, 1, 0, 1066367, 501264863]\) | \(32740359775271/45410156250\) | \(-186000000000000000000\) | \([2]\) | \(5308416\) | \(2.5750\) |
Rank
sage: E.rank()
The elliptic curves in class 148800.ge have rank \(0\).
Complex multiplication
The elliptic curves in class 148800.ge do not have complex multiplication.Modular form 148800.2.a.ge
sage: E.q_eigenform(10)
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.