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SageMath
E = EllipticCurve("en1")
E.isogeny_class()
Elliptic curves in class 91728en
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 91728.ft3 | 91728en1 | \([0, 0, 0, 95109, -107354198]\) | \(270840023/14329224\) | \(-5033828185784745984\) | \([]\) | \(1990656\) | \(2.2683\) | \(\Gamma_0(N)\)-optimal |
| 91728.ft2 | 91728en2 | \([0, 0, 0, -857451, 2926549402]\) | \(-198461344537/10417365504\) | \(-3659599996179619774464\) | \([]\) | \(5971968\) | \(2.8176\) | |
| 91728.ft1 | 91728en3 | \([0, 0, 0, -183854811, 959550064522]\) | \(-1956469094246217097/36641439744\) | \(-12872065657643470946304\) | \([]\) | \(17915904\) | \(3.3669\) |
Rank
sage: E.rank()
The elliptic curves in class 91728en have rank \(0\).
Complex multiplication
The elliptic curves in class 91728en do not have complex multiplication.Modular form 91728.2.a.en
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.
\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
