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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 21840.g
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 21840.g1 | 21840bb4 | \([0, -1, 0, -66396, 4853196]\) | \(126449185587012304/33791748046875\) | \(8650687500000000\) | \([2]\) | \(124416\) | \(1.7664\) | |
| 21840.g2 | 21840bb2 | \([0, -1, 0, -23556, -1383300]\) | \(5646857395652944/2031631875\) | \(520097760000\) | \([2]\) | \(41472\) | \(1.2170\) | |
| 21840.g3 | 21840bb1 | \([0, -1, 0, -1261, -27764]\) | \(-13870539341824/13420809675\) | \(-214732954800\) | \([2]\) | \(20736\) | \(0.87047\) | \(\Gamma_0(N)\)-optimal |
| 21840.g4 | 21840bb3 | \([0, -1, 0, 10499, 485560]\) | \(7998456195055616/11086576921875\) | \(-177385230750000\) | \([2]\) | \(62208\) | \(1.4198\) |
Rank
sage: E.rank()
The elliptic curves in class 21840.g have rank \(1\).
Complex multiplication
The elliptic curves in class 21840.g do not have complex multiplication.Modular form 21840.2.a.g
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.
\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
