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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 1995.b
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 1995.b1 | 1995c4 | \([1, 1, 1, -53200, 4700810]\) | \(16651720753282540801/9975\) | \(9975\) | \([4]\) | \(2816\) | \(0.99091\) | |
| 1995.b2 | 1995c5 | \([1, 1, 1, -14475, -608220]\) | \(335414091635204401/37448756505405\) | \(37448756505405\) | \([2]\) | \(5632\) | \(1.3375\) | |
| 1995.b3 | 1995c3 | \([1, 1, 1, -3450, 66510]\) | \(4541390686576801/633623960025\) | \(633623960025\) | \([2, 2]\) | \(2816\) | \(0.99091\) | |
| 1995.b4 | 1995c2 | \([1, 1, 1, -3325, 72410]\) | \(4065433152958801/99500625\) | \(99500625\) | \([2, 4]\) | \(1408\) | \(0.64434\) | |
| 1995.b5 | 1995c1 | \([1, 1, 1, -200, 1160]\) | \(-885012508801/155859375\) | \(-155859375\) | \([4]\) | \(704\) | \(0.29776\) | \(\Gamma_0(N)\)-optimal |
| 1995.b6 | 1995c6 | \([1, 1, 1, 5575, 366140]\) | \(19162556947522799/68270261146605\) | \(-68270261146605\) | \([2]\) | \(5632\) | \(1.3375\) |
Rank
sage: E.rank()
The elliptic curves in class 1995.b have rank \(0\).
Complex multiplication
The elliptic curves in class 1995.b do not have complex multiplication.Modular form 1995.2.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.
\(\left(\begin{array}{rrrrrr} 1 & 8 & 4 & 2 & 4 & 8 \\ 8 & 1 & 2 & 4 & 8 & 4 \\ 4 & 2 & 1 & 2 & 4 & 2 \\ 2 & 4 & 2 & 1 & 2 & 4 \\ 4 & 8 & 4 & 2 & 1 & 8 \\ 8 & 4 & 2 & 4 & 8 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
