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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 6336.i
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
6336.i1 | 6336cm2 | \([0, 0, 0, -2784, -56864]\) | \(-199794688/1331\) | \(-15897378816\) | \([]\) | \(5760\) | \(0.79289\) | |
6336.i2 | 6336cm1 | \([0, 0, 0, 96, -416]\) | \(8192/11\) | \(-131383296\) | \([]\) | \(1920\) | \(0.24359\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 6336.i have rank \(0\).
Complex multiplication
The elliptic curves in class 6336.i do not have complex multiplication.Modular form 6336.2.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.