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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 6897f
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 6897.a3 | 6897f1 | \([1, 0, 0, -184, 815]\) | \(389017/57\) | \(100978977\) | \([2]\) | \(2160\) | \(0.26079\) | \(\Gamma_0(N)\)-optimal |
| 6897.a2 | 6897f2 | \([1, 0, 0, -789, -7776]\) | \(30664297/3249\) | \(5755801689\) | \([2, 2]\) | \(4320\) | \(0.60737\) | |
| 6897.a1 | 6897f3 | \([1, 0, 0, -12284, -525051]\) | \(115714886617/1539\) | \(2726432379\) | \([2]\) | \(8640\) | \(0.95394\) | |
| 6897.a4 | 6897f4 | \([1, 0, 0, 1026, -37905]\) | \(67419143/390963\) | \(-692614803243\) | \([2]\) | \(8640\) | \(0.95394\) |
Rank
sage: E.rank()
The elliptic curves in class 6897f have rank \(0\).
Complex multiplication
The elliptic curves in class 6897f do not have complex multiplication.Modular form 6897.2.a.f
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.
