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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 30926j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
30926.k2 | 30926j1 | \([1, -1, 1, 3685302, -2097351031]\) | \(513518298333039/473314623488\) | \(-5101960244941713047552\) | \([2]\) | \(2331648\) | \(2.8526\) | \(\Gamma_0(N)\)-optimal |
30926.k1 | 30926j2 | \([1, -1, 1, -18934858, -18836269431]\) | \(69650253363839121/26080144197632\) | \(281123490117645259900928\) | \([2]\) | \(4663296\) | \(3.1992\) |
Rank
sage: E.rank()
The elliptic curves in class 30926j have rank \(0\).
Complex multiplication
The elliptic curves in class 30926j do not have complex multiplication.Modular form 30926.2.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 Cremona 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 Cremona labels.