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SageMath
E = EllipticCurve("cc1")
E.isogeny_class()
Elliptic curves in class 277970.cc
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 277970.cc1 | 277970cc3 | \([1, -1, 1, -7548217, 7983940489]\) | \(1010962818911303721/57392720\) | \(2700091075386320\) | \([2]\) | \(7077888\) | \(2.4276\) | |
| 277970.cc2 | 277970cc4 | \([1, -1, 1, -790297, -63575479]\) | \(1160306142246441/634128110000\) | \(29833115601814910000\) | \([2]\) | \(7077888\) | \(2.4276\) | |
| 277970.cc3 | 277970cc2 | \([1, -1, 1, -472617, 124364009]\) | \(248158561089321/1859334400\) | \(87474024921606400\) | \([2, 2]\) | \(3538944\) | \(2.0810\) | |
| 277970.cc4 | 277970cc1 | \([1, -1, 1, -10537, 4408041]\) | \(-2749884201/176619520\) | \(-8309220920197120\) | \([2]\) | \(1769472\) | \(1.7345\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 277970.cc have rank \(1\).
Complex multiplication
The elliptic curves in class 277970.cc do not have complex multiplication.Modular form 277970.2.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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
