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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 152880.j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
152880.j1 | 152880dx2 | \([0, -1, 0, -18636, 580140]\) | \(69291952/26325\) | \(271951028294400\) | \([2]\) | \(602112\) | \(1.4691\) | |
152880.j2 | 152880dx1 | \([0, -1, 0, 3659, 62896]\) | \(8388608/7605\) | \(-4910226899760\) | \([2]\) | \(301056\) | \(1.1225\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 152880.j have rank \(0\).
Complex multiplication
The elliptic curves in class 152880.j do not have complex multiplication.Modular form 152880.2.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.