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SageMath
E = EllipticCurve("jc1")
E.isogeny_class()
Elliptic curves in class 141120.jc
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
141120.jc1 | 141120fs2 | \([0, 0, 0, -17052, -839664]\) | \(10536048/245\) | \(12750817443840\) | \([2]\) | \(294912\) | \(1.3006\) | |
141120.jc2 | 141120fs1 | \([0, 0, 0, -2352, 24696]\) | \(442368/175\) | \(569232921600\) | \([2]\) | \(147456\) | \(0.95403\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 141120.jc have rank \(0\).
Complex multiplication
The elliptic curves in class 141120.jc do not have complex multiplication.Modular form 141120.2.a.jc
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.