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SageMath
E = EllipticCurve("ba1")
E.isogeny_class()
Elliptic curves in class 2790.ba
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 2790.ba1 | 2790z3 | \([1, -1, 1, -59657, -5593359]\) | \(32208729120020809/658986840\) | \(480401406360\) | \([2]\) | \(9216\) | \(1.3610\) | |
| 2790.ba2 | 2790z2 | \([1, -1, 1, -3857, -80319]\) | \(8702409880009/1120910400\) | \(817143681600\) | \([2, 2]\) | \(4608\) | \(1.0145\) | |
| 2790.ba3 | 2790z1 | \([1, -1, 1, -977, 10689]\) | \(141339344329/17141760\) | \(12496343040\) | \([4]\) | \(2304\) | \(0.66789\) | \(\Gamma_0(N)\)-optimal |
| 2790.ba4 | 2790z4 | \([1, -1, 1, 5863, -426351]\) | \(30579142915511/124675335000\) | \(-90888319215000\) | \([2]\) | \(9216\) | \(1.3610\) |
Rank
sage: E.rank()
The elliptic curves in class 2790.ba have rank \(0\).
Complex multiplication
The elliptic curves in class 2790.ba do not have complex multiplication.Modular form 2790.2.a.ba
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.
