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SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 35739.t
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
35739.t1 | 35739q4 | \([1, -1, 0, -476046, 126416565]\) | \(347873904937/395307\) | \(13557625672660443\) | \([2]\) | \(345600\) | \(2.0089\) | |
35739.t2 | 35739q2 | \([1, -1, 0, -37431, 884952]\) | \(169112377/88209\) | \(3025255315387041\) | \([2, 2]\) | \(172800\) | \(1.6623\) | |
35739.t3 | 35739q1 | \([1, -1, 0, -21186, -1171665]\) | \(30664297/297\) | \(10186044832953\) | \([2]\) | \(86400\) | \(1.3157\) | \(\Gamma_0(N)\)-optimal |
35739.t4 | 35739q3 | \([1, -1, 0, 141264, 6781887]\) | \(9090072503/5845851\) | \(-200491920447013899\) | \([2]\) | \(345600\) | \(2.0089\) |
Rank
sage: E.rank()
The elliptic curves in class 35739.t have rank \(1\).
Complex multiplication
The elliptic curves in class 35739.t do not have complex multiplication.Modular form 35739.2.a.t
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.