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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 28830g
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 28830.h3 | 28830g1 | \([1, 1, 0, -234023, -43668123]\) | \(1597099875769/186000\) | \(165075684666000\) | \([2]\) | \(276480\) | \(1.7544\) | \(\Gamma_0(N)\)-optimal |
| 28830.h2 | 28830g2 | \([1, 1, 0, -253243, -36099287]\) | \(2023804595449/540562500\) | \(479751208560562500\) | \([2, 2]\) | \(552960\) | \(2.1010\) | |
| 28830.h4 | 28830g3 | \([1, 1, 0, 640487, -232898633]\) | \(32740359775271/45410156250\) | \(-40301680826660156250\) | \([2]\) | \(1105920\) | \(2.4476\) | |
| 28830.h1 | 28830g4 | \([1, 1, 0, -1454493, 645489963]\) | \(383432500775449/18701300250\) | \(16597472811361220250\) | \([2]\) | \(1105920\) | \(2.4476\) |
Rank
sage: E.rank()
The elliptic curves in class 28830g have rank \(0\).
Complex multiplication
The elliptic curves in class 28830g do not have complex multiplication.Modular form 28830.2.a.g
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 Cremona 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 Cremona labels.
