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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 5776.i
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality | CM discriminant |
---|---|---|---|---|---|---|---|---|---|
5776.i1 | 5776g2 | \([0, 0, 0, -219488, 39617584]\) | \(-884736\) | \(-1321728810102784\) | \([]\) | \(27360\) | \(1.8152\) | \(-19\) | |
5776.i2 | 5776g1 | \([0, 0, 0, -608, -5776]\) | \(-884736\) | \(-28094464\) | \([]\) | \(1440\) | \(0.34300\) | \(\Gamma_0(N)\)-optimal | \(-19\) |
Rank
sage: E.rank()
The elliptic curves in class 5776.i have rank \(0\).
Complex multiplication
Each elliptic curve in class 5776.i has complex multiplication by an order in the imaginary quadratic field \(\Q(\sqrt{-19}) \).Modular form 5776.2.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.
\(\left(\begin{array}{rr} 1 & 19 \\ 19 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.