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SageMath
E = EllipticCurve("cn1")
E.isogeny_class()
Elliptic curves in class 115920.cn
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 115920.cn1 | 115920ef4 | \([0, 0, 0, -646707, -200170766]\) | \(10017490085065009/235066440\) | \(701904628776960\) | \([2]\) | \(1179648\) | \(1.9607\) | |
| 115920.cn2 | 115920ef3 | \([0, 0, 0, -174387, 25121266]\) | \(196416765680689/22365315000\) | \(66782472744960000\) | \([2]\) | \(1179648\) | \(1.9607\) | |
| 115920.cn3 | 115920ef2 | \([0, 0, 0, -41907, -2885006]\) | \(2725812332209/373262400\) | \(1114555554201600\) | \([2, 2]\) | \(589824\) | \(1.6142\) | |
| 115920.cn4 | 115920ef1 | \([0, 0, 0, 4173, -240014]\) | \(2691419471/9891840\) | \(-29536875970560\) | \([2]\) | \(294912\) | \(1.2676\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 115920.cn have rank \(2\).
Complex multiplication
The elliptic curves in class 115920.cn do not have complex multiplication.Modular form 115920.2.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 LMFDB numbering.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
