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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 78897.f
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 78897.f1 | 78897m4 | \([1, 0, 0, -7153334, -7364546781]\) | \(1677087406638588673/4641\) | \(112022457729\) | \([2]\) | \(1474560\) | \(2.2385\) | |
| 78897.f2 | 78897m2 | \([1, 0, 0, -447089, -115095936]\) | \(409460675852593/21538881\) | \(519896226320289\) | \([2, 2]\) | \(737280\) | \(1.8920\) | |
| 78897.f3 | 78897m3 | \([1, 0, 0, -422524, -128297167]\) | \(-345608484635233/94427721297\) | \(-2279255638319106993\) | \([4]\) | \(1474560\) | \(2.2385\) | |
| 78897.f4 | 78897m1 | \([1, 0, 0, -29484, -1590897]\) | \(117433042273/22801233\) | \(550366334822577\) | \([2]\) | \(368640\) | \(1.5454\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 78897.f have rank \(0\).
Complex multiplication
The elliptic curves in class 78897.f do not have complex multiplication.Modular form 78897.2.a.f
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.
