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SageMath
E = EllipticCurve("cn1")
E.isogeny_class()
Elliptic curves in class 78650cn
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
78650.dh2 | 78650cn1 | \([1, 1, 1, -15793, 959311]\) | \(-9836106385/3407872\) | \(-150931328204800\) | \([]\) | \(486000\) | \(1.4320\) | \(\Gamma_0(N)\)-optimal |
78650.dh1 | 78650cn2 | \([1, 1, 1, -1370993, 617304271]\) | \(-6434774386429585/140608\) | \(-6227391227200\) | \([]\) | \(1458000\) | \(1.9813\) |
Rank
sage: E.rank()
The elliptic curves in class 78650cn have rank \(0\).
Complex multiplication
The elliptic curves in class 78650cn do not have complex multiplication.Modular form 78650.2.a.cn
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 Cremona 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 Cremona labels.