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SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 27930t
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 27930.n4 | 27930t1 | \([1, 1, 0, 180148, 176706384]\) | \(5495662324535111/117739817533440\) | \(-13851971792991682560\) | \([2]\) | \(645120\) | \(2.3532\) | \(\Gamma_0(N)\)-optimal |
| 27930.n3 | 27930t2 | \([1, 1, 0, -3833932, 2735280976]\) | \(52974743974734147769/3152005008998400\) | \(370830237303652761600\) | \([2, 2]\) | \(1290240\) | \(2.6998\) | |
| 27930.n2 | 27930t3 | \([1, 1, 0, -11454412, -11525685296]\) | \(1412712966892699019449/330160465517040000\) | \(38843048607614238960000\) | \([2]\) | \(2580480\) | \(3.0464\) | |
| 27930.n1 | 27930t4 | \([1, 1, 0, -60438732, 180825302736]\) | \(207530301091125281552569/805586668007040\) | \(94776465904360248960\) | \([2]\) | \(2580480\) | \(3.0464\) |
Rank
sage: E.rank()
The elliptic curves in class 27930t have rank \(0\).
Complex multiplication
The elliptic curves in class 27930t do not have complex multiplication.Modular form 27930.2.a.t
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
