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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 3536.j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
3536.j1 | 3536i2 | \([0, 0, 0, -187483, -31245750]\) | \(177930109857804849/634933\) | \(2600685568\) | \([2]\) | \(15360\) | \(1.4483\) | |
3536.j2 | 3536i1 | \([0, 0, 0, -11723, -487750]\) | \(43499078731809/82055753\) | \(336100364288\) | \([2]\) | \(7680\) | \(1.1017\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 3536.j have rank \(1\).
Complex multiplication
The elliptic curves in class 3536.j do not have complex multiplication.Modular form 3536.2.a.j
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.