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SageMath
E = EllipticCurve("hq1")
E.isogeny_class()
Elliptic curves in class 152880.hq
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 152880.hq1 | 152880p3 | \([0, 1, 0, -67838360, 215038122900]\) | \(71647584155243142409/10140000\) | \(4886367682560000\) | \([2]\) | \(8847360\) | \(2.8634\) | |
| 152880.hq2 | 152880p4 | \([0, 1, 0, -4867480, 2298807188]\) | \(26465989780414729/10571870144160\) | \(5094481717617786224640\) | \([2]\) | \(8847360\) | \(2.8634\) | |
| 152880.hq3 | 152880p2 | \([0, 1, 0, -4240280, 3358273428]\) | \(17496824387403529/6580454400\) | \(3171057171274137600\) | \([2, 2]\) | \(4423680\) | \(2.5168\) | |
| 152880.hq4 | 152880p1 | \([0, 1, 0, -226200, 68333460]\) | \(-2656166199049/2658140160\) | \(-1280931969777008640\) | \([2]\) | \(2211840\) | \(2.1702\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 152880.hq have rank \(0\).
Complex multiplication
The elliptic curves in class 152880.hq do not have complex multiplication.Modular form 152880.2.a.hq
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.
