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SageMath
E = EllipticCurve("fc1")
E.isogeny_class()
Elliptic curves in class 149058.fc
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
149058.fc1 | 149058p3 | \([1, -1, 1, -31080146, 66698261907]\) | \(8020417344913/187278\) | \(77528725564342376142\) | \([2]\) | \(12386304\) | \(2.9287\) | |
149058.fc2 | 149058p2 | \([1, -1, 1, -2013836, 961895211]\) | \(2181825073/298116\) | \(123413073347320517124\) | \([2, 2]\) | \(6193152\) | \(2.5821\) | |
149058.fc3 | 149058p1 | \([1, -1, 1, -523256, -130401813]\) | \(38272753/4368\) | \(1808250158935099152\) | \([2]\) | \(3096576\) | \(2.2356\) | \(\Gamma_0(N)\)-optimal |
149058.fc4 | 149058p4 | \([1, -1, 1, 3203194, 5114651091]\) | \(8780064047/32388174\) | \(-13407948897233893324686\) | \([2]\) | \(12386304\) | \(2.9287\) |
Rank
sage: E.rank()
The elliptic curves in class 149058.fc have rank \(0\).
Complex multiplication
The elliptic curves in class 149058.fc do not have complex multiplication.Modular form 149058.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.