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SageMath
E = EllipticCurve("cc1")
E.isogeny_class()
Elliptic curves in class 11466cc
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 11466.cl3 | 11466cc1 | \([1, -1, 1, 5944, 1675923]\) | \(270840023/14329224\) | \(-1228961959420104\) | \([]\) | \(82944\) | \(1.5751\) | \(\Gamma_0(N)\)-optimal |
| 11466.cl2 | 11466cc2 | \([1, -1, 1, -53591, -45713937]\) | \(-198461344537/10417365504\) | \(-893457030317289984\) | \([]\) | \(248832\) | \(2.1244\) | |
| 11466.cl1 | 11466cc3 | \([1, -1, 1, -11490926, -14990097027]\) | \(-1956469094246217097/36641439744\) | \(-3142594154698113024\) | \([]\) | \(746496\) | \(2.6737\) |
Rank
sage: E.rank()
The elliptic curves in class 11466cc have rank \(0\).
Complex multiplication
The elliptic curves in class 11466cc do not have complex multiplication.Modular form 11466.2.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 Cremona numbering.
\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
