Show commands:
SageMath
E = EllipticCurve("ci1")
E.isogeny_class()
Elliptic curves in class 54150.ci
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 54150.ci1 | 54150ct4 | \([1, 0, 0, -27436188, -55316121258]\) | \(3107086841064961/570\) | \(419002377656250\) | \([2]\) | \(3317760\) | \(2.6415\) | |
| 54150.ci2 | 54150ct3 | \([1, 0, 0, -1985688, -573178758]\) | \(1177918188481/488703750\) | \(359242163543027343750\) | \([2]\) | \(3317760\) | \(2.6415\) | |
| 54150.ci3 | 54150ct2 | \([1, 0, 0, -1714938, -864235008]\) | \(758800078561/324900\) | \(238831355264062500\) | \([2, 2]\) | \(1658880\) | \(2.2949\) | |
| 54150.ci4 | 54150ct1 | \([1, 0, 0, -90438, -17870508]\) | \(-111284641/123120\) | \(-90504513573750000\) | \([4]\) | \(829440\) | \(1.9483\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 54150.ci have rank \(0\).
Complex multiplication
The elliptic curves in class 54150.ci do not have complex multiplication.Modular form 54150.2.a.ci
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.
