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SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 159936.t
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
159936.t1 | 159936cu3 | \([0, -1, 0, -1197017537, -15940535323551]\) | \(-6150311179917589675873/244053849830826\) | \(-7526859768790213741510656\) | \([]\) | \(89579520\) | \(3.8568\) | |
159936.t2 | 159936cu2 | \([0, -1, 0, -3048257, -55329087519]\) | \(-101566487155393/42823570577256\) | \(-1320720860405718356852736\) | \([]\) | \(29859840\) | \(3.3075\) | |
159936.t3 | 159936cu1 | \([0, -1, 0, 338623, 2046691809]\) | \(139233463487/58763045376\) | \(-1812309875213211795456\) | \([]\) | \(9953280\) | \(2.7582\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 159936.t have rank \(0\).
Complex multiplication
The elliptic curves in class 159936.t do not have complex multiplication.Modular form 159936.2.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.
\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.