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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 33488.p
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 33488.p1 | 33488f4 | \([0, 0, 0, -15851, 227386]\) | \(215062038362754/113550802729\) | \(232552043988992\) | \([4]\) | \(71680\) | \(1.4482\) | |
| 33488.p2 | 33488f2 | \([0, 0, 0, -9091, -330990]\) | \(81144432781668/740329681\) | \(758097593344\) | \([2, 2]\) | \(35840\) | \(1.1017\) | |
| 33488.p3 | 33488f1 | \([0, 0, 0, -9071, -332530]\) | \(322440248841552/27209\) | \(6965504\) | \([2]\) | \(17920\) | \(0.75509\) | \(\Gamma_0(N)\)-optimal |
| 33488.p4 | 33488f3 | \([0, 0, 0, -2651, -790806]\) | \(-1006057824354/131332646081\) | \(-268969259173888\) | \([2]\) | \(71680\) | \(1.4482\) |
Rank
sage: E.rank()
The elliptic curves in class 33488.p have rank \(1\).
Complex multiplication
The elliptic curves in class 33488.p do not have complex multiplication.Modular form 33488.2.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.
