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SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 97020.t
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
97020.t1 | 97020l2 | \([0, 0, 0, -15436008, 23342674068]\) | \(-1647408715474378752/3025\) | \(-746883244800\) | \([]\) | \(1928448\) | \(2.4248\) | |
97020.t2 | 97020l1 | \([0, 0, 0, -190008, 32217668]\) | \(-2239956387422208/27680640625\) | \(-9375100812000000\) | \([]\) | \(642816\) | \(1.8754\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 97020.t have rank \(2\).
Complex multiplication
The elliptic curves in class 97020.t do not have complex multiplication.Modular form 97020.2.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.