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SageMath
E = EllipticCurve("v1")
E.isogeny_class()
Elliptic curves in class 16320.v
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 16320.v1 | 16320p4 | \([0, -1, 0, -107889505, 431373110497]\) | \(1059623036730633329075378/154307373046875\) | \(20225376000000000000\) | \([4]\) | \(1720320\) | \(3.1129\) | |
| 16320.v2 | 16320p3 | \([0, -1, 0, -12542625, -6443985375]\) | \(1664865424893526702418/826424127435466125\) | \(108321063231221415936000\) | \([2]\) | \(1720320\) | \(3.1129\) | |
| 16320.v3 | 16320p2 | \([0, -1, 0, -6762625, 6700890625]\) | \(521902963282042184836/6241849278890625\) | \(409065834341376000000\) | \([2, 2]\) | \(860160\) | \(2.7664\) | |
| 16320.v4 | 16320p1 | \([0, -1, 0, -80945, 269105457]\) | \(-3579968623693264/1906997690433375\) | \(-31244250160060416000\) | \([2]\) | \(430080\) | \(2.4198\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 16320.v have rank \(0\).
Complex multiplication
The elliptic curves in class 16320.v do not have complex multiplication.Modular form 16320.2.a.v
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.
