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SageMath
E = EllipticCurve("cr1")
E.isogeny_class()
Elliptic curves in class 18480cr
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 18480.cf3 | 18480cr1 | \([0, 1, 0, -3174696, 2170736820]\) | \(863913648706111516969/2486234429521920\) | \(10183616223321784320\) | \([2]\) | \(602112\) | \(2.5184\) | \(\Gamma_0(N)\)-optimal |
| 18480.cf2 | 18480cr2 | \([0, 1, 0, -4485416, 206229684]\) | \(2436531580079063806249/1405478914998681600\) | \(5756841635834599833600\) | \([2, 2]\) | \(1204224\) | \(2.8649\) | |
| 18480.cf1 | 18480cr3 | \([0, 1, 0, -47851816, -126961401676]\) | \(2958414657792917260183849/12401051653985258880\) | \(50794707574723620372480\) | \([2]\) | \(2408448\) | \(3.2115\) | |
| 18480.cf4 | 18480cr4 | \([0, 1, 0, 17909464, 1666375860]\) | \(155099895405729262880471/90047655797243760000\) | \(-368835198145510440960000\) | \([2]\) | \(2408448\) | \(3.2115\) |
Rank
sage: E.rank()
The elliptic curves in class 18480cr have rank \(0\).
Complex multiplication
The elliptic curves in class 18480cr do not have complex multiplication.Modular form 18480.2.a.cr
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.
