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SageMath
E = EllipticCurve("dq1")
E.isogeny_class()
Elliptic curves in class 371280.dq
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 371280.dq1 | 371280dq4 | \([0, 1, 0, -40127653816, -3093966743929516]\) | \(1744596788171434949302427839201849/9588363813082031250000\) | \(39273938178384000000000000\) | \([2]\) | \(622854144\) | \(4.5251\) | |
| 371280.dq2 | 371280dq3 | \([0, 1, 0, -3442349496, -9131894978220]\) | \(1101358349464662961278219354169/628567168199833707765102000\) | \(2574611120946518867005857792000\) | \([2]\) | \(622854144\) | \(4.5251\) | |
| 371280.dq3 | 371280dq2 | \([0, 1, 0, -2509389496, -48286733442220]\) | \(426646307804307769001905914169/998470877001641316000000\) | \(4089736712198722830336000000\) | \([2, 2]\) | \(311427072\) | \(4.1785\) | |
| 371280.dq4 | 371280dq1 | \([0, 1, 0, -99937976, -1309175266476]\) | \(-26949791983733109138764089/165161952797784563712000\) | \(-676503358659725572964352000\) | \([2]\) | \(155713536\) | \(3.8319\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 371280.dq have rank \(1\).
Complex multiplication
The elliptic curves in class 371280.dq do not have complex multiplication.Modular form 371280.2.a.dq
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.
