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SageMath
E = EllipticCurve("fj1")
E.isogeny_class()
Elliptic curves in class 193600.fj
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 193600.fj1 | 193600db1 | \([0, 0, 0, -459800, -115797000]\) | \(379275264/15125\) | \(428717762000000000\) | \([2]\) | \(2211840\) | \(2.1498\) | \(\Gamma_0(N)\)-optimal |
| 193600.fj2 | 193600db2 | \([0, 0, 0, 205700, -423258000]\) | \(2122416/171875\) | \(-77948684000000000000\) | \([2]\) | \(4423680\) | \(2.4964\) |
Rank
sage: E.rank()
The elliptic curves in class 193600.fj have rank \(1\).
Complex multiplication
The elliptic curves in class 193600.fj do not have complex multiplication.Modular form 193600.2.a.fj
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.
