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SageMath
E = EllipticCurve("di1")
E.isogeny_class()
Elliptic curves in class 86640.di
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 86640.di1 | 86640eh4 | \([0, 1, 0, -17559160, 28314830420]\) | \(3107086841064961/570\) | \(109838959288320\) | \([2]\) | \(3317760\) | \(2.5299\) | |
| 86640.di2 | 86640eh3 | \([0, 1, 0, -1270840, 292959188]\) | \(1177918188481/488703750\) | \(94173177719823360000\) | \([2]\) | \(3317760\) | \(2.5299\) | |
| 86640.di3 | 86640eh2 | \([0, 1, 0, -1097560, 442049300]\) | \(758800078561/324900\) | \(62608206794342400\) | \([2, 2]\) | \(1658880\) | \(2.1833\) | |
| 86640.di4 | 86640eh1 | \([0, 1, 0, -57880, 9126548]\) | \(-111284641/123120\) | \(-23725215206277120\) | \([2]\) | \(829440\) | \(1.8367\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 86640.di have rank \(1\).
Complex multiplication
The elliptic curves in class 86640.di do not have complex multiplication.Modular form 86640.2.a.di
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.
