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SageMath
E = EllipticCurve("cc1")
E.isogeny_class()
Elliptic curves in class 67600cc
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 67600.m3 | 67600cc1 | \([0, 1, 0, -5633, -113762]\) | \(16384/5\) | \(6033511250000\) | \([2]\) | \(110592\) | \(1.1572\) | \(\Gamma_0(N)\)-optimal |
| 67600.m4 | 67600cc2 | \([0, 1, 0, 15492, -747512]\) | \(21296/25\) | \(-482680900000000\) | \([2]\) | \(221184\) | \(1.5038\) | |
| 67600.m1 | 67600cc3 | \([0, 1, 0, -174633, 28024738]\) | \(488095744/125\) | \(150837781250000\) | \([2]\) | \(331776\) | \(1.7066\) | |
| 67600.m2 | 67600cc4 | \([0, 1, 0, -153508, 35080488]\) | \(-20720464/15625\) | \(-301675562500000000\) | \([2]\) | \(663552\) | \(2.0531\) |
Rank
sage: E.rank()
The elliptic curves in class 67600cc have rank \(0\).
Complex multiplication
The elliptic curves in class 67600cc do not have complex multiplication.Modular form 67600.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
