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SageMath
E = EllipticCurve("fc1")
E.isogeny_class()
Elliptic curves in class 172480.fc
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 172480.fc1 | 172480gv1 | \([0, 1, 0, -277601, -56926465]\) | \(-76711450249/851840\) | \(-26271579939799040\) | \([]\) | \(1257984\) | \(1.9655\) | \(\Gamma_0(N)\)-optimal |
| 172480.fc2 | 172480gv2 | \([0, 1, 0, 929759, -294293441]\) | \(2882081488391/2883584000\) | \(-88932554903650304000\) | \([]\) | \(3773952\) | \(2.5148\) |
Rank
sage: E.rank()
The elliptic curves in class 172480.fc have rank \(0\).
Complex multiplication
The elliptic curves in class 172480.fc do not have complex multiplication.Modular form 172480.2.a.fc
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.
