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SageMath
E = EllipticCurve("ba1")
E.isogeny_class()
Elliptic curves in class 28175.ba
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 28175.ba1 | 28175i4 | \([1, -1, 0, -151517, -22657734]\) | \(209267191953/55223\) | \(101514542609375\) | \([2]\) | \(122880\) | \(1.6720\) | |
| 28175.ba2 | 28175i2 | \([1, -1, 0, -10642, -258609]\) | \(72511713/25921\) | \(47649683265625\) | \([2, 2]\) | \(61440\) | \(1.3255\) | |
| 28175.ba3 | 28175i1 | \([1, -1, 0, -4517, 115016]\) | \(5545233/161\) | \(295960765625\) | \([2]\) | \(30720\) | \(0.97889\) | \(\Gamma_0(N)\)-optimal |
| 28175.ba4 | 28175i3 | \([1, -1, 0, 32233, -1844984]\) | \(2014698447/1958887\) | \(-3600954635359375\) | \([2]\) | \(122880\) | \(1.6720\) |
Rank
sage: E.rank()
The elliptic curves in class 28175.ba have rank \(1\).
Complex multiplication
The elliptic curves in class 28175.ba do not have complex multiplication.Modular form 28175.2.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.
