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SageMath
E = EllipticCurve("fd1")
E.isogeny_class()
Elliptic curves in class 141120.fd
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 141120.fd1 | 141120ef1 | \([0, 0, 0, -53508, -4302592]\) | \(140608/15\) | \(1807428372664320\) | \([2]\) | \(573440\) | \(1.6619\) | \(\Gamma_0(N)\)-optimal |
| 141120.fd2 | 141120ef2 | \([0, 0, 0, 69972, -21244048]\) | \(39304/225\) | \(-216891404719718400\) | \([2]\) | \(1146880\) | \(2.0085\) |
Rank
sage: E.rank()
The elliptic curves in class 141120.fd have rank \(0\).
Complex multiplication
The elliptic curves in class 141120.fd do not have complex multiplication.Modular form 141120.2.a.fd
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.
