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SageMath
E = EllipticCurve("fa1")
E.isogeny_class()
Elliptic curves in class 14400.fa
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 14400.fa1 | 14400fe2 | \([0, 0, 0, -484500, -129800000]\) | \(2156689088/81\) | \(472392000000000\) | \([2]\) | \(122880\) | \(1.9021\) | |
| 14400.fa2 | 14400fe1 | \([0, 0, 0, -28875, -2225000]\) | \(-29218112/6561\) | \(-597871125000000\) | \([2]\) | \(61440\) | \(1.5555\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 14400.fa have rank \(0\).
Complex multiplication
The elliptic curves in class 14400.fa do not have complex multiplication.Modular form 14400.2.a.fa
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
