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SageMath
E = EllipticCurve("w1")
E.isogeny_class()
Elliptic curves in class 4650.w
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 4650.w1 | 4650z3 | \([1, 1, 1, -37838, -2726719]\) | \(383432500775449/18701300250\) | \(292207816406250\) | \([2]\) | \(27648\) | \(1.5353\) | |
| 4650.w2 | 4650z2 | \([1, 1, 1, -6588, 148281]\) | \(2023804595449/540562500\) | \(8446289062500\) | \([2, 2]\) | \(13824\) | \(1.1887\) | |
| 4650.w3 | 4650z1 | \([1, 1, 1, -6088, 180281]\) | \(1597099875769/186000\) | \(2906250000\) | \([4]\) | \(6912\) | \(0.84216\) | \(\Gamma_0(N)\)-optimal |
| 4650.w4 | 4650z4 | \([1, 1, 1, 16662, 985281]\) | \(32740359775271/45410156250\) | \(-709533691406250\) | \([2]\) | \(27648\) | \(1.5353\) |
Rank
sage: E.rank()
The elliptic curves in class 4650.w have rank \(0\).
Complex multiplication
The elliptic curves in class 4650.w do not have complex multiplication.Modular form 4650.2.a.w
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.
