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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 16650.i
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
16650.i1 | 16650l2 | \([1, -1, 0, -15879492, 24359726416]\) | \(62202232222815625/232783872\) | \(1657221120000000000\) | \([]\) | \(1088640\) | \(2.7113\) | |
16650.i2 | 16650l1 | \([1, -1, 0, -270117, 5979541]\) | \(306163065625/175056768\) | \(1246253748750000000\) | \([]\) | \(362880\) | \(2.1620\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 16650.i have rank \(0\).
Complex multiplication
The elliptic curves in class 16650.i do not have complex multiplication.Modular form 16650.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.