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SageMath
E = EllipticCurve("jl1")
E.isogeny_class()
Elliptic curves in class 270480jl
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
270480.jl4 | 270480jl1 | \([0, 1, 0, -18440, 64308]\) | \(1439069689/828345\) | \(399171423866880\) | \([2]\) | \(1081344\) | \(1.4913\) | \(\Gamma_0(N)\)-optimal |
270480.jl2 | 270480jl2 | \([0, 1, 0, -210520, 37020500]\) | \(2141202151369/5832225\) | \(2810492678246400\) | \([2, 2]\) | \(2162688\) | \(1.8379\) | |
270480.jl1 | 270480jl3 | \([0, 1, 0, -3366120, 2375951220]\) | \(8753151307882969/65205\) | \(31421657272320\) | \([4]\) | \(4325376\) | \(2.1844\) | |
270480.jl3 | 270480jl4 | \([0, 1, 0, -128200, 66359348]\) | \(-483551781049/3672913125\) | \(-1769941222371840000\) | \([2]\) | \(4325376\) | \(2.1844\) |
Rank
sage: E.rank()
The elliptic curves in class 270480jl have rank \(1\).
Complex multiplication
The elliptic curves in class 270480jl do not have complex multiplication.Modular form 270480.2.a.jl
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.