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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 29624.o
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
29624.o1 | 29624j2 | \([0, -1, 0, -258328, -50446596]\) | \(12576878500/1127\) | \(170840521628672\) | \([2]\) | \(168960\) | \(1.7710\) | |
29624.o2 | 29624j1 | \([0, -1, 0, -14988, -902572]\) | \(-9826000/3703\) | \(-140333285623552\) | \([2]\) | \(84480\) | \(1.4244\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 29624.o have rank \(1\).
Complex multiplication
The elliptic curves in class 29624.o do not have complex multiplication.Modular form 29624.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.