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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 45177.c
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 45177.c1 | 45177a4 | \([1, 1, 1, -200587, 34460654]\) | \(347873904937/395307\) | \(1014249609562563\) | \([2]\) | \(304128\) | \(1.7928\) | |
| 45177.c2 | 45177a2 | \([1, 1, 1, -15772, 232916]\) | \(169112377/88209\) | \(226320160811481\) | \([2, 2]\) | \(152064\) | \(1.4463\) | |
| 45177.c3 | 45177a1 | \([1, 1, 1, -8927, -325636]\) | \(30664297/297\) | \(762020743473\) | \([2]\) | \(76032\) | \(1.0997\) | \(\Gamma_0(N)\)-optimal |
| 45177.c4 | 45177a3 | \([1, 1, 1, 59523, 1889406]\) | \(9090072503/5845851\) | \(-14998854293779059\) | \([2]\) | \(304128\) | \(1.7928\) |
Rank
sage: E.rank()
The elliptic curves in class 45177.c have rank \(0\).
Complex multiplication
The elliptic curves in class 45177.c do not have complex multiplication.Modular form 45177.2.a.c
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.
