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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 10608l
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 10608.r4 | 10608l1 | \([0, 1, 0, -39, -264]\) | \(-420616192/1456611\) | \(-23305776\) | \([2]\) | \(3072\) | \(0.099727\) | \(\Gamma_0(N)\)-optimal |
| 10608.r3 | 10608l2 | \([0, 1, 0, -884, -10404]\) | \(298766385232/439569\) | \(112529664\) | \([2, 2]\) | \(6144\) | \(0.44630\) | |
| 10608.r1 | 10608l3 | \([0, 1, 0, -14144, -652188]\) | \(305612563186948/663\) | \(678912\) | \([2]\) | \(12288\) | \(0.79287\) | |
| 10608.r2 | 10608l4 | \([0, 1, 0, -1144, -4060]\) | \(161838334948/87947613\) | \(90058355712\) | \([4]\) | \(12288\) | \(0.79287\) |
Rank
sage: E.rank()
The elliptic curves in class 10608l have rank \(0\).
Complex multiplication
The elliptic curves in class 10608l do not have complex multiplication.Modular form 10608.2.a.l
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.
