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Rank
The elliptic curves in class 487305.cx have rank \(0\).
Complex multiplication
The elliptic curves in class 487305.cx do not have complex multiplication.Modular form 487305.2.a.cx
Isogeny 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
The vertices are labelled with LMFDB labels.
Elliptic curves in class 487305.cx
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 487305.cx1 | 487305cx4 | \([1, -1, 0, -6882255, -6947627324]\) | \(420339554066191969/244298925\) | \(20952571161719925\) | \([2]\) | \(9437184\) | \(2.4564\) | |
| 487305.cx2 | 487305cx2 | \([1, -1, 0, -432630, -107155049]\) | \(104413920565969/2472575625\) | \(212063220235400625\) | \([2, 2]\) | \(4718592\) | \(2.1098\) | |
| 487305.cx3 | 487305cx1 | \([1, -1, 0, -59985, 3222400]\) | \(278317173889/109245825\) | \(9369590645694825\) | \([2]\) | \(2359296\) | \(1.7633\) | \(\Gamma_0(N)\)-optimal* |
| 487305.cx4 | 487305cx3 | \([1, -1, 0, 54675, -335311250]\) | \(210751100351/566398828125\) | \(-48577830427226953125\) | \([2]\) | \(9437184\) | \(2.4564\) |