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SageMath
E = EllipticCurve("eh1")
E.isogeny_class()
Elliptic curves in class 129360eh
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
129360.cc3 | 129360eh1 | \([0, -1, 0, -12734136, -17486260560]\) | \(473897054735271721/779625\) | \(375693728256000\) | \([2]\) | \(3538944\) | \(2.4884\) | \(\Gamma_0(N)\)-optimal |
129360.cc2 | 129360eh2 | \([0, -1, 0, -12738056, -17474952144]\) | \(474334834335054841/607815140625\) | \(292900222891584000000\) | \([2, 2]\) | \(7077888\) | \(2.8350\) | |
129360.cc4 | 129360eh3 | \([0, -1, 0, -9308056, -27100904144]\) | \(-185077034913624841/551466161890875\) | \(-265746196399306968576000\) | \([2]\) | \(14155776\) | \(3.1816\) | |
129360.cc1 | 129360eh4 | \([0, -1, 0, -16230776, -7125324240]\) | \(981281029968144361/522287841796875\) | \(251685446859000000000000\) | \([2]\) | \(14155776\) | \(3.1816\) |
Rank
sage: E.rank()
The elliptic curves in class 129360eh have rank \(0\).
Complex multiplication
The elliptic curves in class 129360eh do not have complex multiplication.Modular form 129360.2.a.eh
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 Cremona numbering.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.