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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 36400.i
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
36400.i1 | 36400bn2 | \([0, 1, 0, -2250008, 1211043988]\) | \(19683218700810001/1478750000000\) | \(94640000000000000000\) | \([2]\) | \(1290240\) | \(2.5784\) | |
36400.i2 | 36400bn1 | \([0, 1, 0, -458008, -97116012]\) | \(166021325905681/32614400000\) | \(2087321600000000000\) | \([2]\) | \(645120\) | \(2.2318\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 36400.i have rank \(1\).
Complex multiplication
The elliptic curves in class 36400.i do not have complex multiplication.Modular form 36400.2.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.