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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 54096.l
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 54096.l1 | 54096f4 | \([0, -1, 0, -36864, 2317680]\) | \(45989074372/7555707\) | \(910255485791232\) | \([2]\) | \(221184\) | \(1.5920\) | |
| 54096.l2 | 54096f2 | \([0, -1, 0, -10404, -370656]\) | \(4135597648/385641\) | \(11614791170304\) | \([2, 2]\) | \(110592\) | \(1.2455\) | |
| 54096.l3 | 54096f1 | \([0, -1, 0, -10159, -390746]\) | \(61604313088/621\) | \(1168960464\) | \([2]\) | \(55296\) | \(0.89888\) | \(\Gamma_0(N)\)-optimal |
| 54096.l4 | 54096f3 | \([0, -1, 0, 12136, -1777152]\) | \(1640689628/12223143\) | \(-1472553524026368\) | \([2]\) | \(221184\) | \(1.5920\) |
Rank
sage: E.rank()
The elliptic curves in class 54096.l have rank \(0\).
Complex multiplication
The elliptic curves in class 54096.l do not have complex multiplication.Modular form 54096.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
