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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 262080p
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 262080.p4 | 262080p1 | \([0, 0, 0, -278508, -5883568]\) | \(12501706118329/7156531200\) | \(1367634410156851200\) | \([2]\) | \(3932160\) | \(2.1697\) | \(\Gamma_0(N)\)-optimal |
| 262080.p2 | 262080p2 | \([0, 0, 0, -3227628, -2227160752]\) | \(19458380202497209/47698560000\) | \(9115336766914560000\) | \([2, 2]\) | \(7864320\) | \(2.5163\) | |
| 262080.p3 | 262080p3 | \([0, 0, 0, -2029548, -3901118128]\) | \(-4837870546133689/31603162500000\) | \(-6039458404761600000000\) | \([2]\) | \(15728640\) | \(2.8628\) | |
| 262080.p1 | 262080p4 | \([0, 0, 0, -51611628, -142714943152]\) | \(79560762543506753209/479824800\) | \(91695947238604800\) | \([2]\) | \(15728640\) | \(2.8628\) |
Rank
sage: E.rank()
The elliptic curves in class 262080p have rank \(0\).
Complex multiplication
The elliptic curves in class 262080p do not have complex multiplication.Modular form 262080.2.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 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.
