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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 2400.a
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 2400.a1 | 2400v2 | \([0, -1, 0, -90033, -10368063]\) | \(1261112198464/675\) | \(43200000000\) | \([2]\) | \(9216\) | \(1.3704\) | |
| 2400.a2 | 2400v3 | \([0, -1, 0, -12408, 300312]\) | \(26410345352/10546875\) | \(84375000000000\) | \([2]\) | \(9216\) | \(1.3704\) | |
| 2400.a3 | 2400v1 | \([0, -1, 0, -5658, -158688]\) | \(20034997696/455625\) | \(455625000000\) | \([2, 2]\) | \(4608\) | \(1.0238\) | \(\Gamma_0(N)\)-optimal |
| 2400.a4 | 2400v4 | \([0, -1, 0, 592, -496188]\) | \(2863288/13286025\) | \(-106288200000000\) | \([2]\) | \(9216\) | \(1.3704\) |
Rank
sage: E.rank()
The elliptic curves in class 2400.a have rank \(0\).
Complex multiplication
The elliptic curves in class 2400.a do not have complex multiplication.Modular form 2400.2.a.a
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.
