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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 159120.e
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
159120.e1 | 159120en2 | \([0, 0, 0, -12243, -214542]\) | \(3670232225814/1764381125\) | \(97563218688000\) | \([2]\) | \(430080\) | \(1.3780\) | |
159120.e2 | 159120en1 | \([0, 0, 0, 2757, -25542]\) | \(83824368372/58703125\) | \(-1623024000000\) | \([2]\) | \(215040\) | \(1.0315\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 159120.e have rank \(1\).
Complex multiplication
The elliptic curves in class 159120.e do not have complex multiplication.Modular form 159120.2.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.