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SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 37030.t
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
37030.t1 | 37030s1 | \([1, -1, 1, -712927, -76405049]\) | \(270701905514769/139540889600\) | \(20657059643786854400\) | \([2]\) | \(811008\) | \(2.3983\) | \(\Gamma_0(N)\)-optimal |
37030.t2 | 37030s2 | \([1, -1, 1, 2672673, -595078969]\) | \(14262456319278831/9284810958080\) | \(-1374485244376314533120\) | \([2]\) | \(1622016\) | \(2.7449\) |
Rank
sage: E.rank()
The elliptic curves in class 37030.t have rank \(1\).
Complex multiplication
The elliptic curves in class 37030.t do not have complex multiplication.Modular form 37030.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.