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SageMath
E = EllipticCurve("fx1")
E.isogeny_class()
Elliptic curves in class 304200fx
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 304200.fx2 | 304200fx1 | \([0, 0, 0, -22815, -2965950]\) | \(-432\) | \(-3040194609504000\) | \([2]\) | \(1658880\) | \(1.6593\) | \(\Gamma_0(N)\)-optimal |
| 304200.fx1 | 304200fx2 | \([0, 0, 0, -479115, -127535850]\) | \(1000188\) | \(12160778438016000\) | \([2]\) | \(3317760\) | \(2.0059\) |
Rank
sage: E.rank()
The elliptic curves in class 304200fx have rank \(1\).
Complex multiplication
The elliptic curves in class 304200fx do not have complex multiplication.Modular form 304200.2.a.fx
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 Cremona 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 Cremona labels.
