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SageMath
E = EllipticCurve("cc1")
E.isogeny_class()
Elliptic curves in class 177744.cc
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 177744.cc1 | 177744ck3 | \([0, 1, 0, -2133104, 1198418916]\) | \(7080974546692/189\) | \(28650273813504\) | \([2]\) | \(2365440\) | \(2.0959\) | |
| 177744.cc2 | 177744ck4 | \([0, 1, 0, -207544, -4433980]\) | \(6522128932/3720087\) | \(563923339471199232\) | \([2]\) | \(2365440\) | \(2.0959\) | |
| 177744.cc3 | 177744ck2 | \([0, 1, 0, -133484, 18643116]\) | \(6940769488/35721\) | \(1353725437688064\) | \([2, 2]\) | \(1182720\) | \(1.7494\) | |
| 177744.cc4 | 177744ck1 | \([0, 1, 0, -3879, 602100]\) | \(-2725888/64827\) | \(-153547561219248\) | \([2]\) | \(591360\) | \(1.4028\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 177744.cc have rank \(0\).
Complex multiplication
The elliptic curves in class 177744.cc do not have complex multiplication.Modular form 177744.2.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.
