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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 39039l
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
39039.e4 | 39039l1 | \([1, 1, 1, 1771, 184322]\) | \(127263527/3090087\) | \(-14915259742383\) | \([4]\) | \(75264\) | \(1.2080\) | \(\Gamma_0(N)\)-optimal |
39039.e3 | 39039l2 | \([1, 1, 1, -39634, 2867366]\) | \(1426487591593/81162081\) | \(391753863029529\) | \([2, 2]\) | \(150528\) | \(1.5546\) | |
39039.e2 | 39039l3 | \([1, 1, 1, -116529, -11742684]\) | \(36254831403673/8741423691\) | \(42193182544532019\) | \([2]\) | \(301056\) | \(1.9011\) | |
39039.e1 | 39039l4 | \([1, 1, 1, -625219, 190020332]\) | \(5599640476399033/19792773\) | \(95535934851357\) | \([2]\) | \(301056\) | \(1.9011\) |
Rank
sage: E.rank()
The elliptic curves in class 39039l have rank \(0\).
Complex multiplication
The elliptic curves in class 39039l do not have complex multiplication.Modular form 39039.2.a.l
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.