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SageMath
E = EllipticCurve("jk1")
E.isogeny_class()
Elliptic curves in class 78400.jk
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
78400.jk1 | 78400ci2 | \([0, -1, 0, -19273, 1037457]\) | \(-262885120/343\) | \(-1033052339200\) | \([]\) | \(165888\) | \(1.2123\) | |
78400.jk2 | 78400ci1 | \([0, -1, 0, 327, 6497]\) | \(1280/7\) | \(-21082700800\) | \([]\) | \(55296\) | \(0.66304\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 78400.jk have rank \(0\).
Complex multiplication
The elliptic curves in class 78400.jk do not have complex multiplication.Modular form 78400.2.a.jk
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.