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SageMath
E = EllipticCurve("iz1")
E.isogeny_class()
Elliptic curves in class 248430iz
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 248430.iz3 | 248430iz1 | \([1, 0, 0, -29156, 1207296]\) | \(4826809/1680\) | \(954020343428880\) | \([2]\) | \(1769472\) | \(1.5759\) | \(\Gamma_0(N)\)-optimal |
| 248430.iz2 | 248430iz2 | \([1, 0, 0, -194776, -32214820]\) | \(1439069689/44100\) | \(25043034015008100\) | \([2, 2]\) | \(3538944\) | \(1.9224\) | |
| 248430.iz4 | 248430iz3 | \([1, 0, 0, 53654, -108681574]\) | \(30080231/9003750\) | \(-5112952778064153750\) | \([2]\) | \(7077888\) | \(2.2690\) | |
| 248430.iz1 | 248430iz4 | \([1, 0, 0, -3093126, -2094101010]\) | \(5763259856089/5670\) | \(3219818659072470\) | \([2]\) | \(7077888\) | \(2.2690\) |
Rank
sage: E.rank()
The elliptic curves in class 248430iz have rank \(0\).
Complex multiplication
The elliptic curves in class 248430iz do not have complex multiplication.Modular form 248430.2.a.iz
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.
