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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 1104.e
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
1104.e1 | 1104i2 | \([0, 1, 0, -504, -4524]\) | \(3463512697/3174\) | \(13000704\) | \([2]\) | \(384\) | \(0.28860\) | |
1104.e2 | 1104i1 | \([0, 1, 0, -24, -108]\) | \(-389017/828\) | \(-3391488\) | \([2]\) | \(192\) | \(-0.057978\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 1104.e have rank \(0\).
Complex multiplication
The elliptic curves in class 1104.e do not have complex multiplication.Modular form 1104.2.a.e
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.