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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 46800.j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
46800.j1 | 46800el1 | \([0, 0, 0, -3027675, -2027461750]\) | \(65787589563409/10400000\) | \(485222400000000000\) | \([2]\) | \(1105920\) | \(2.4041\) | \(\Gamma_0(N)\)-optimal |
46800.j2 | 46800el2 | \([0, 0, 0, -2739675, -2428645750]\) | \(-48743122863889/26406250000\) | \(-1232010000000000000000\) | \([2]\) | \(2211840\) | \(2.7507\) |
Rank
sage: E.rank()
The elliptic curves in class 46800.j have rank \(0\).
Complex multiplication
The elliptic curves in class 46800.j do not have complex multiplication.Modular form 46800.2.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.