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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 12495.b
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 12495.b1 | 12495a5 | \([1, 1, 1, -1135331, 465139898]\) | \(1375634265228629281/24990412335\) | \(2940097020800415\) | \([2]\) | \(196608\) | \(2.0942\) | |
| 12495.b2 | 12495a3 | \([1, 1, 1, -280526, -57304276]\) | \(20751759537944401/418359375\) | \(49219562109375\) | \([2]\) | \(98304\) | \(1.7476\) | |
| 12495.b3 | 12495a4 | \([1, 1, 1, -73256, 6748328]\) | \(369543396484081/45120132225\) | \(5308338436139025\) | \([2, 2]\) | \(98304\) | \(1.7476\) | |
| 12495.b4 | 12495a2 | \([1, 1, 1, -18131, -836872]\) | \(5602762882081/716900625\) | \(84342641630625\) | \([2, 2]\) | \(49152\) | \(1.4011\) | |
| 12495.b5 | 12495a1 | \([1, 1, 1, 1714, -66886]\) | \(4733169839/19518975\) | \(-2296387889775\) | \([2]\) | \(24576\) | \(1.0545\) | \(\Gamma_0(N)\)-optimal |
| 12495.b6 | 12495a6 | \([1, 1, 1, 106819, 34912058]\) | \(1145725929069119/5127181719135\) | \(-603207802074513615\) | \([2]\) | \(196608\) | \(2.0942\) |
Rank
sage: E.rank()
The elliptic curves in class 12495.b have rank \(0\).
Complex multiplication
The elliptic curves in class 12495.b do not have complex multiplication.Modular form 12495.2.a.b
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.
\(\left(\begin{array}{rrrrrr} 1 & 8 & 2 & 4 & 8 & 4 \\ 8 & 1 & 4 & 2 & 4 & 8 \\ 2 & 4 & 1 & 2 & 4 & 2 \\ 4 & 2 & 2 & 1 & 2 & 4 \\ 8 & 4 & 4 & 2 & 1 & 8 \\ 4 & 8 & 2 & 4 & 8 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
