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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 16560q
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 16560.bp4 | 16560q1 | \([0, 0, 0, -35607, -16553194]\) | \(-26752376766544/618796614375\) | \(-115482299361120000\) | \([2]\) | \(98304\) | \(1.9547\) | \(\Gamma_0(N)\)-optimal |
| 16560.bp3 | 16560q2 | \([0, 0, 0, -1216587, -514218166]\) | \(266763091319403556/1355769140625\) | \(1012076240400000000\) | \([2, 2]\) | \(196608\) | \(2.3013\) | |
| 16560.bp1 | 16560q3 | \([0, 0, 0, -19441587, -32994813166]\) | \(544328872410114151778/14166950625\) | \(21151143947520000\) | \([2]\) | \(393216\) | \(2.6479\) | |
| 16560.bp2 | 16560q4 | \([0, 0, 0, -1887267, 115818626]\) | \(497927680189263938/284271240234375\) | \(424414687500000000000\) | \([2]\) | \(393216\) | \(2.6479\) |
Rank
sage: E.rank()
The elliptic curves in class 16560q have rank \(1\).
Complex multiplication
The elliptic curves in class 16560q do not have complex multiplication.Modular form 16560.2.a.q
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
