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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 38115.o
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 38115.o1 | 38115bd4 | \([1, -1, 1, -959432, 361955454]\) | \(75627935783569/396165\) | \(511634407938885\) | \([2]\) | \(368640\) | \(2.0184\) | |
| 38115.o2 | 38115bd2 | \([1, -1, 1, -61007, 5460414]\) | \(19443408769/1334025\) | \(1722850557345225\) | \([2, 2]\) | \(184320\) | \(1.6718\) | |
| 38115.o3 | 38115bd1 | \([1, -1, 1, -12002, -400584]\) | \(148035889/31185\) | \(40274428613265\) | \([2]\) | \(92160\) | \(1.3253\) | \(\Gamma_0(N)\)-optimal |
| 38115.o4 | 38115bd3 | \([1, -1, 1, 53338, 23481186]\) | \(12994449551/192163125\) | \(-248172520760443125\) | \([2]\) | \(368640\) | \(2.0184\) |
Rank
sage: E.rank()
The elliptic curves in class 38115.o have rank \(1\).
Complex multiplication
The elliptic curves in class 38115.o do not have complex multiplication.Modular form 38115.2.a.o
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.
