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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 48510.p
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 48510.p1 | 48510y4 | \([1, -1, 0, -808311555, -8844587929899]\) | \(680995599504466943307169/52207031250000000\) | \(4477594559238281250000000\) | \([2]\) | \(20643840\) | \(3.7783\) | |
| 48510.p2 | 48510y2 | \([1, -1, 0, -53884035, -118728348075]\) | \(201738262891771037089/45727545600000000\) | \(3921874208962617600000000\) | \([2, 2]\) | \(10321920\) | \(3.4318\) | |
| 48510.p3 | 48510y1 | \([1, -1, 0, -17757315, 27216375381]\) | \(7220044159551112609/448454983680000\) | \(38462244393351905280000\) | \([2]\) | \(5160960\) | \(3.0852\) | \(\Gamma_0(N)\)-optimal |
| 48510.p4 | 48510y3 | \([1, -1, 0, 122515965, -733764588075]\) | \(2371297246710590562911/4084000833203280000\) | \(-350268909624613330076880000\) | \([2]\) | \(20643840\) | \(3.7783\) |
Rank
sage: E.rank()
The elliptic curves in class 48510.p have rank \(0\).
Complex multiplication
The elliptic curves in class 48510.p do not have complex multiplication.Modular form 48510.2.a.p
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
