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SageMath
E = EllipticCurve("jv1")
E.isogeny_class()
Elliptic curves in class 145200.jv
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
145200.jv1 | 145200im1 | \([0, 1, 0, -24249408, -45970162812]\) | \(55635379958596/24057\) | \(681895087632000000\) | \([2]\) | \(6451200\) | \(2.7644\) | \(\Gamma_0(N)\)-optimal |
145200.jv2 | 145200im2 | \([0, 1, 0, -24128408, -46451500812]\) | \(-27403349188178/578739249\) | \(-32808700246326048000000\) | \([2]\) | \(12902400\) | \(3.1110\) |
Rank
sage: E.rank()
The elliptic curves in class 145200.jv have rank \(1\).
Complex multiplication
The elliptic curves in class 145200.jv do not have complex multiplication.Modular form 145200.2.a.jv
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.