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SageMath
E = EllipticCurve("ba1")
E.isogeny_class()
Elliptic curves in class 340704ba
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 340704.ba3 | 340704ba1 | \([0, 0, 0, -21801, -1142440]\) | \(5088448/441\) | \(99313023910464\) | \([2, 2]\) | \(983040\) | \(1.4266\) | \(\Gamma_0(N)\)-optimal |
| 340704.ba2 | 340704ba2 | \([0, 0, 0, -75036, 6608576]\) | \(3241792/567\) | \(8172043110346752\) | \([2]\) | \(1966080\) | \(1.7731\) | |
| 340704.ba4 | 340704ba3 | \([0, 0, 0, 23829, -5294770]\) | \(830584/7203\) | \(-12976901790967296\) | \([2]\) | \(1966080\) | \(1.7731\) | |
| 340704.ba1 | 340704ba4 | \([0, 0, 0, -341211, -76714846]\) | \(2438569736/21\) | \(37833532918272\) | \([2]\) | \(1966080\) | \(1.7731\) |
Rank
sage: E.rank()
The elliptic curves in class 340704ba have rank \(1\).
Complex multiplication
The elliptic curves in class 340704ba do not have complex multiplication.Modular form 340704.2.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 Cremona numbering.
\(\left(\begin{array}{rrrr} 1 & 2 & 2 & 2 \\ 2 & 1 & 4 & 4 \\ 2 & 4 & 1 & 4 \\ 2 & 4 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
