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SageMath
E = EllipticCurve("fw1")
E.isogeny_class()
Elliptic curves in class 158400.fw
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 158400.fw1 | 158400dm1 | \([0, 0, 0, -840, 9830]\) | \(-56197120/3267\) | \(-3810628800\) | \([]\) | \(82944\) | \(0.59467\) | \(\Gamma_0(N)\)-optimal |
| 158400.fw2 | 158400dm2 | \([0, 0, 0, 4560, 17390]\) | \(8990228480/5314683\) | \(-6199046251200\) | \([]\) | \(248832\) | \(1.1440\) |
Rank
sage: E.rank()
The elliptic curves in class 158400.fw have rank \(2\).
Complex multiplication
The elliptic curves in class 158400.fw do not have complex multiplication.Modular form 158400.2.a.fw
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
