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SageMath
E = EllipticCurve("cr1")
E.isogeny_class()
Elliptic curves in class 152592.cr
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
152592.cr1 | 152592t1 | \([0, 1, 0, -915648, -337533900]\) | \(858729462625/38148\) | \(3771596727140352\) | \([2]\) | \(1769472\) | \(2.0662\) | \(\Gamma_0(N)\)-optimal |
152592.cr2 | 152592t2 | \([0, 1, 0, -869408, -373101708]\) | \(-735091890625/181908738\) | \(-17984858993368768512\) | \([2]\) | \(3538944\) | \(2.4128\) |
Rank
sage: E.rank()
The elliptic curves in class 152592.cr have rank \(0\).
Complex multiplication
The elliptic curves in class 152592.cr do not have complex multiplication.Modular form 152592.2.a.cr
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.