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SageMath
E = EllipticCurve("fc1")
E.isogeny_class()
Elliptic curves in class 377520fc
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 377520.fc3 | 377520fc1 | \([0, 1, 0, -26176, 1572404]\) | \(273359449/9360\) | \(67919097692160\) | \([2]\) | \(1105920\) | \(1.4260\) | \(\Gamma_0(N)\)-optimal |
| 377520.fc2 | 377520fc2 | \([0, 1, 0, -64896, -4204620]\) | \(4165509529/1368900\) | \(9933168037478400\) | \([2, 2]\) | \(2211840\) | \(1.7726\) | |
| 377520.fc4 | 377520fc3 | \([0, 1, 0, 186784, -28667916]\) | \(99317171591/106616250\) | \(-773640972149760000\) | \([2]\) | \(4423680\) | \(2.1191\) | |
| 377520.fc1 | 377520fc4 | \([0, 1, 0, -936096, -348851340]\) | \(12501706118329/2570490\) | \(18652282203709440\) | \([2]\) | \(4423680\) | \(2.1191\) |
Rank
sage: E.rank()
The elliptic curves in class 377520fc have rank \(1\).
Complex multiplication
The elliptic curves in class 377520fc do not have complex multiplication.Modular form 377520.2.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 Cremona numbering.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
