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SageMath
E = EllipticCurve("fp1")
E.isogeny_class()
Elliptic curves in class 310464.fp
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 310464.fp1 | 310464fp4 | \([0, 0, 0, -67089036, -211507207184]\) | \(2970658109581346/2139291\) | \(24048918955322376192\) | \([2]\) | \(25165824\) | \(3.0308\) | |
| 310464.fp2 | 310464fp3 | \([0, 0, 0, -9653196, 6856405360]\) | \(8849350367426/3314597517\) | \(37261170666284195119104\) | \([2]\) | \(25165824\) | \(3.0308\) | |
| 310464.fp3 | 310464fp2 | \([0, 0, 0, -4220076, -3260064080]\) | \(1478729816932/38900169\) | \(218648844787675889664\) | \([2, 2]\) | \(12582912\) | \(2.6842\) | |
| 310464.fp4 | 310464fp1 | \([0, 0, 0, 48804, -164272304]\) | \(9148592/8301447\) | \(-11665127962658193408\) | \([2]\) | \(6291456\) | \(2.3376\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 310464.fp have rank \(0\).
Complex multiplication
The elliptic curves in class 310464.fp do not have complex multiplication.Modular form 310464.2.a.fp
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
