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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 97020.j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
97020.j1 | 97020g2 | \([0, 0, 0, -20223, 1115478]\) | \(-3704530032/33275\) | \(-8215715692800\) | \([]\) | \(248832\) | \(1.3014\) | |
97020.j2 | 97020g1 | \([0, 0, 0, 777, 8078]\) | \(153174672/171875\) | \(-58212000000\) | \([]\) | \(82944\) | \(0.75207\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 97020.j have rank \(1\).
Complex multiplication
The elliptic curves in class 97020.j do not have complex multiplication.Modular form 97020.2.a.j
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.