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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 364650.i
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
364650.i1 | 364650i2 | \([1, 1, 0, -9375, -349125]\) | \(5832972054001/80587650\) | \(1259182031250\) | \([2]\) | \(835584\) | \(1.1275\) | |
364650.i2 | 364650i1 | \([1, 1, 0, -1125, 5625]\) | \(10091699281/4813380\) | \(75209062500\) | \([2]\) | \(417792\) | \(0.78088\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 364650.i have rank \(2\).
Complex multiplication
The elliptic curves in class 364650.i do not have complex multiplication.Modular form 364650.2.a.i
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.