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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 2310l
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 2310.l7 | 2310l1 | \([1, 0, 1, -1173, 6928]\) | \(178272935636041/81841914000\) | \(81841914000\) | \([6]\) | \(2304\) | \(0.78883\) | \(\Gamma_0(N)\)-optimal |
| 2310.l5 | 2310l2 | \([1, 0, 1, -15753, 759256]\) | \(432288716775559561/270140062500\) | \(270140062500\) | \([2, 6]\) | \(4608\) | \(1.1354\) | |
| 2310.l4 | 2310l3 | \([1, 0, 1, -47748, -4019582]\) | \(12038605770121350841/757333463040\) | \(757333463040\) | \([2]\) | \(6912\) | \(1.3381\) | |
| 2310.l2 | 2310l4 | \([1, 0, 1, -252003, 48670756]\) | \(1769857772964702379561/691787250\) | \(691787250\) | \([6]\) | \(9216\) | \(1.4820\) | |
| 2310.l6 | 2310l5 | \([1, 0, 1, -12783, 1055068]\) | \(-230979395175477481/348191894531250\) | \(-348191894531250\) | \([6]\) | \(9216\) | \(1.4820\) | |
| 2310.l3 | 2310l6 | \([1, 0, 1, -50628, -3508094]\) | \(14351050585434661561/3001282273281600\) | \(3001282273281600\) | \([2, 2]\) | \(13824\) | \(1.6847\) | |
| 2310.l1 | 2310l7 | \([1, 0, 1, -256428, 46871746]\) | \(1864737106103260904761/129177711985836360\) | \(129177711985836360\) | \([2]\) | \(27648\) | \(2.0313\) | |
| 2310.l8 | 2310l8 | \([1, 0, 1, 109092, -21141182]\) | \(143584693754978072519/276341298967965000\) | \(-276341298967965000\) | \([2]\) | \(27648\) | \(2.0313\) |
Rank
sage: E.rank()
The elliptic curves in class 2310l have rank \(0\).
Complex multiplication
The elliptic curves in class 2310l do not have complex multiplication.Modular form 2310.2.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.
\(\left(\begin{array}{rrrrrrrr} 1 & 2 & 3 & 4 & 4 & 6 & 12 & 12 \\ 2 & 1 & 6 & 2 & 2 & 3 & 6 & 6 \\ 3 & 6 & 1 & 12 & 12 & 2 & 4 & 4 \\ 4 & 2 & 12 & 1 & 4 & 6 & 3 & 12 \\ 4 & 2 & 12 & 4 & 1 & 6 & 12 & 3 \\ 6 & 3 & 2 & 6 & 6 & 1 & 2 & 2 \\ 12 & 6 & 4 & 3 & 12 & 2 & 1 & 4 \\ 12 & 6 & 4 & 12 & 3 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
