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SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 77616.t
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
77616.t1 | 77616cv2 | \([0, 0, 0, -47512899, 126056548674]\) | \(-61279455929796531/681472\) | \(-131914160192618496\) | \([]\) | \(3732480\) | \(2.8541\) | |
77616.t2 | 77616cv1 | \([0, 0, 0, -555219, 192226706]\) | \(-71285434106859/18863581528\) | \(-5008873061235326976\) | \([]\) | \(1244160\) | \(2.3048\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 77616.t have rank \(0\).
Complex multiplication
The elliptic curves in class 77616.t do not have complex multiplication.Modular form 77616.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.