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SageMath
E = EllipticCurve("ca1")
E.isogeny_class()
Elliptic curves in class 27930.ca
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 27930.ca1 | 27930ch4 | \([1, 1, 1, -148961, -22190827]\) | \(3107086841064961/570\) | \(67059930\) | \([2]\) | \(110592\) | \(1.3375\) | |
| 27930.ca2 | 27930ch3 | \([1, 1, 1, -10781, -233731]\) | \(1177918188481/488703750\) | \(57495507483750\) | \([2]\) | \(110592\) | \(1.3375\) | |
| 27930.ca3 | 27930ch2 | \([1, 1, 1, -9311, -349567]\) | \(758800078561/324900\) | \(38224160100\) | \([2, 2]\) | \(55296\) | \(0.99090\) | |
| 27930.ca4 | 27930ch1 | \([1, 1, 1, -491, -7351]\) | \(-111284641/123120\) | \(-14484944880\) | \([2]\) | \(27648\) | \(0.64432\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 27930.ca have rank \(0\).
Complex multiplication
The elliptic curves in class 27930.ca do not have complex multiplication.Modular form 27930.2.a.ca
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.
