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SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 91035.r
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
91035.r1 | 91035bh2 | \([1, -1, 1, -3253688492, 63270172598784]\) | \(216486375407331255135001/27004994294227023375\) | \(475187651665581576138054348375\) | \([2]\) | \(92897280\) | \(4.4241\) | |
91035.r2 | 91035bh1 | \([1, -1, 1, 301553383, 5117792297784]\) | \(172343644217341694999/742780064187984375\) | \(-13070171782297026428591109375\) | \([2]\) | \(46448640\) | \(4.0775\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 91035.r have rank \(1\).
Complex multiplication
The elliptic curves in class 91035.r do not have complex multiplication.Modular form 91035.2.a.r
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.