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SageMath
E = EllipticCurve("v1")
E.isogeny_class()
Elliptic curves in class 167310v
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 167310.fq4 | 167310v1 | \([1, -1, 1, 98833, 15510759]\) | \(30342134159/47190000\) | \(-166049518081590000\) | \([4]\) | \(2752512\) | \(1.9895\) | \(\Gamma_0(N)\)-optimal |
| 167310.fq3 | 167310v2 | \([1, -1, 1, -661667, 157572159]\) | \(9104453457841/2226896100\) | \(7835876758270232100\) | \([2, 2]\) | \(5505024\) | \(2.3361\) | |
| 167310.fq1 | 167310v3 | \([1, -1, 1, -9863717, 11925153699]\) | \(30161840495801041/2799263610\) | \(9849891363081837210\) | \([2]\) | \(11010048\) | \(2.6827\) | |
| 167310.fq2 | 167310v4 | \([1, -1, 1, -3627617, -2527205781]\) | \(1500376464746641/83599963590\) | \(294166850302139661990\) | \([2]\) | \(11010048\) | \(2.6827\) |
Rank
sage: E.rank()
The elliptic curves in class 167310v have rank \(0\).
Complex multiplication
The elliptic curves in class 167310v do not have complex multiplication.Modular form 167310.2.a.v
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 Cremona 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 Cremona labels.
