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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 206856.l
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 206856.l1 | 206856g4 | \([0, 0, 0, -21513531, -38407466266]\) | \(305612563186948/663\) | \(2388917364268032\) | \([2]\) | \(8257536\) | \(2.6247\) | |
| 206856.l2 | 206856g3 | \([0, 0, 0, -1740531, -218210434]\) | \(161838334948/87947613\) | \(316892277287518712832\) | \([2]\) | \(8257536\) | \(2.6247\) | |
| 206856.l3 | 206856g2 | \([0, 0, 0, -1345071, -599671150]\) | \(298766385232/439569\) | \(395963053127426304\) | \([2, 2]\) | \(4128768\) | \(2.2781\) | |
| 206856.l4 | 206856g1 | \([0, 0, 0, -59826, -14884675]\) | \(-420616192/1456611\) | \(-82007053895263536\) | \([2]\) | \(2064384\) | \(1.9315\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 206856.l have rank \(1\).
Complex multiplication
The elliptic curves in class 206856.l do not have complex multiplication.Modular form 206856.2.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.
