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SageMath
E = EllipticCurve("ta1")
E.isogeny_class()
Elliptic curves in class 369600.ta
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 369600.ta1 | 369600ta4 | \([0, 1, 0, -439605633, -3547797883137]\) | \(9175156963749600923236/50249267578125\) | \(51455250000000000000000\) | \([2]\) | \(70778880\) | \(3.5514\) | |
| 369600.ta2 | 369600ta3 | \([0, 1, 0, -88713633, 257610304863]\) | \(75404081626158563716/15633273575910375\) | \(16008472141732224000000000\) | \([2]\) | \(70778880\) | \(3.5514\) | |
| 369600.ta3 | 369600ta2 | \([0, 1, 0, -27963633, -53368945137]\) | \(9446361110552374864/661910688140625\) | \(169449136164000000000000\) | \([2, 2]\) | \(35389440\) | \(3.2048\) | |
| 369600.ta4 | 369600ta1 | \([0, 1, 0, 1560867, -3620162637]\) | \(26284586405881856/369163298455875\) | \(-5906612775294000000000\) | \([2]\) | \(17694720\) | \(2.8582\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 369600.ta have rank \(0\).
Complex multiplication
The elliptic curves in class 369600.ta do not have complex multiplication.Modular form 369600.2.a.ta
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
