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SageMath
E = EllipticCurve("fb1")
E.isogeny_class()
Elliptic curves in class 39600.fb
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 39600.fb1 | 39600ed4 | \([0, 0, 0, -527475, 147307250]\) | \(347873904937/395307\) | \(18443443392000000\) | \([2]\) | \(393216\) | \(2.0345\) | |
| 39600.fb2 | 39600ed2 | \([0, 0, 0, -41475, 1021250]\) | \(169112377/88209\) | \(4115479104000000\) | \([2, 2]\) | \(196608\) | \(1.6880\) | |
| 39600.fb3 | 39600ed1 | \([0, 0, 0, -23475, -1372750]\) | \(30664297/297\) | \(13856832000000\) | \([2]\) | \(98304\) | \(1.3414\) | \(\Gamma_0(N)\)-optimal |
| 39600.fb4 | 39600ed3 | \([0, 0, 0, 156525, 7951250]\) | \(9090072503/5845851\) | \(-272744024256000000\) | \([2]\) | \(393216\) | \(2.0345\) |
Rank
sage: E.rank()
The elliptic curves in class 39600.fb have rank \(0\).
Complex multiplication
The elliptic curves in class 39600.fb do not have complex multiplication.Modular form 39600.2.a.fb
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
