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SageMath
E = EllipticCurve("cc1")
E.isogeny_class()
Elliptic curves in class 115542.cc
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 115542.cc1 | 115542ce4 | \([1, -1, 1, -2464979, 1490210075]\) | \(19312898130234073/84888\) | \(7280514479448\) | \([2]\) | \(1769472\) | \(2.0964\) | |
| 115542.cc2 | 115542ce2 | \([1, -1, 1, -154139, 23288843]\) | \(4722184089433/9884736\) | \(847775463829056\) | \([2, 2]\) | \(884736\) | \(1.7498\) | |
| 115542.cc3 | 115542ce3 | \([1, -1, 1, -101219, 39482363]\) | \(-1337180541913/7067998104\) | \(-606194780615434584\) | \([2]\) | \(1769472\) | \(2.0964\) | |
| 115542.cc4 | 115542ce1 | \([1, -1, 1, -13019, 88715]\) | \(2845178713/1609728\) | \(138060126425088\) | \([2]\) | \(442368\) | \(1.4032\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 115542.cc have rank \(1\).
Complex multiplication
The elliptic curves in class 115542.cc do not have complex multiplication.Modular form 115542.2.a.cc
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
