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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 152944.e
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
152944.e1 | 152944d2 | \([0, 1, 0, -17464, 755412]\) | \(81182737/12482\) | \(90573309550592\) | \([2]\) | \(368640\) | \(1.4016\) | |
152944.e2 | 152944d1 | \([0, 1, 0, 1896, 66196]\) | \(103823/316\) | \(-2292995178496\) | \([2]\) | \(184320\) | \(1.0551\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 152944.e have rank \(1\).
Complex multiplication
The elliptic curves in class 152944.e do not have complex multiplication.Modular form 152944.2.a.e
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.