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SageMath
E = EllipticCurve("ba1")
E.isogeny_class()
Elliptic curves in class 77400.ba
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 77400.ba1 | 77400ba4 | \([0, 0, 0, -1791075, 29492750]\) | \(54477543627364/31494140625\) | \(367347656250000000000\) | \([2]\) | \(1769472\) | \(2.6356\) | |
| 77400.ba2 | 77400ba2 | \([0, 0, 0, -1210575, -510952750]\) | \(67283921459536/260015625\) | \(758205562500000000\) | \([2, 2]\) | \(884736\) | \(2.2890\) | |
| 77400.ba3 | 77400ba1 | \([0, 0, 0, -1209450, -511952875]\) | \(1073544204384256/16125\) | \(2938781250000\) | \([2]\) | \(442368\) | \(1.9424\) | \(\Gamma_0(N)\)-optimal |
| 77400.ba4 | 77400ba3 | \([0, 0, 0, -648075, -987390250]\) | \(-2580786074884/34615360125\) | \(-403753560498000000000\) | \([2]\) | \(1769472\) | \(2.6356\) |
Rank
sage: E.rank()
The elliptic curves in class 77400.ba have rank \(1\).
Complex multiplication
The elliptic curves in class 77400.ba do not have complex multiplication.Modular form 77400.2.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.
