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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 35280.p
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 35280.p1 | 35280em4 | \([0, 0, 0, -2635563, -1646864422]\) | \(5763259856089/5670\) | \(1991859839262720\) | \([2]\) | \(589824\) | \(2.2290\) | |
| 35280.p2 | 35280em2 | \([0, 0, 0, -165963, -25325062]\) | \(1439069689/44100\) | \(15492243194265600\) | \([2, 2]\) | \(294912\) | \(1.8824\) | |
| 35280.p3 | 35280em1 | \([0, 0, 0, -24843, 951482]\) | \(4826809/1680\) | \(590180693114880\) | \([2]\) | \(147456\) | \(1.5358\) | \(\Gamma_0(N)\)-optimal |
| 35280.p4 | 35280em3 | \([0, 0, 0, 45717, -85484518]\) | \(30080231/9003750\) | \(-3162999652162560000\) | \([2]\) | \(589824\) | \(2.2290\) |
Rank
sage: E.rank()
The elliptic curves in class 35280.p have rank \(2\).
Complex multiplication
The elliptic curves in class 35280.p do not have complex multiplication.Modular form 35280.2.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.
