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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 13680.l
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 13680.l1 | 13680n4 | \([0, 0, 0, -18243, 948402]\) | \(899466517764/95\) | \(70917120\) | \([2]\) | \(16384\) | \(0.93463\) | |
| 13680.l2 | 13680n3 | \([0, 0, 0, -2043, -11718]\) | \(1263284964/651605\) | \(486420526080\) | \([2]\) | \(16384\) | \(0.93463\) | |
| 13680.l3 | 13680n2 | \([0, 0, 0, -1143, 14742]\) | \(884901456/9025\) | \(1684281600\) | \([2, 2]\) | \(8192\) | \(0.58805\) | |
| 13680.l4 | 13680n1 | \([0, 0, 0, -18, 567]\) | \(-55296/11875\) | \(-138510000\) | \([2]\) | \(4096\) | \(0.24148\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 13680.l have rank \(1\).
Complex multiplication
The elliptic curves in class 13680.l do not have complex multiplication.Modular form 13680.2.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 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.
