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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 28749.b
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 28749.b1 | 28749f4 | \([1, 0, 0, -3575172, 1185634485]\) | \(1969718647361977/903077159859\) | \(2317048918414951016331\) | \([2]\) | \(1313280\) | \(2.7944\) | |
| 28749.b2 | 28749f2 | \([1, 0, 0, -1802317, -918744400]\) | \(252352098250057/3961065969\) | \(10163011564454475321\) | \([2, 2]\) | \(656640\) | \(2.4478\) | |
| 28749.b3 | 28749f1 | \([1, 0, 0, -1795472, -926160273]\) | \(249487788397177/62937\) | \(161479123003233\) | \([2]\) | \(328320\) | \(2.1013\) | \(\Gamma_0(N)\)-optimal |
| 28749.b4 | 28749f3 | \([1, 0, 0, -138982, -2548480033]\) | \(-115714886617/1093466116323\) | \(-2805534891996587074107\) | \([2]\) | \(1313280\) | \(2.7944\) |
Rank
sage: E.rank()
The elliptic curves in class 28749.b have rank \(0\).
Complex multiplication
The elliptic curves in class 28749.b do not have complex multiplication.Modular form 28749.2.a.b
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.
