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SageMath
E = EllipticCurve("cs1")
E.isogeny_class()
Elliptic curves in class 161700.cs
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
161700.cs1 | 161700bn1 | \([0, 1, 0, -2750533, -3633432937]\) | \(-4890195460096/9282994875\) | \(-4368540256195500000000\) | \([]\) | \(8957952\) | \(2.8422\) | \(\Gamma_0(N)\)-optimal |
161700.cs2 | 161700bn2 | \([0, 1, 0, 23709467, 76976957063]\) | \(3132137615458304/7250937873795\) | \(-3412262359656431820000000\) | \([]\) | \(26873856\) | \(3.3915\) |
Rank
sage: E.rank()
The elliptic curves in class 161700.cs have rank \(0\).
Complex multiplication
The elliptic curves in class 161700.cs do not have complex multiplication.Modular form 161700.2.a.cs
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.