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SageMath
E = EllipticCurve("dc1")
E.isogeny_class()
Elliptic curves in class 46800.dc
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 46800.dc1 | 46800ba4 | \([0, 0, 0, -2226675, -608840750]\) | \(52337949619538/23423590125\) | \(546425510436000000000\) | \([2]\) | \(1179648\) | \(2.6746\) | |
| 46800.dc2 | 46800ba2 | \([0, 0, 0, -1101675, 438534250]\) | \(12677589459076/213890625\) | \(2494820250000000000\) | \([2, 2]\) | \(589824\) | \(2.3280\) | |
| 46800.dc3 | 46800ba1 | \([0, 0, 0, -1097175, 442345750]\) | \(50091484483024/14625\) | \(42646500000000\) | \([2]\) | \(294912\) | \(1.9814\) | \(\Gamma_0(N)\)-optimal |
| 46800.dc4 | 46800ba3 | \([0, 0, 0, -48675, 1241973250]\) | \(-546718898/28564453125\) | \(-666351562500000000000\) | \([2]\) | \(1179648\) | \(2.6746\) |
Rank
sage: E.rank()
The elliptic curves in class 46800.dc have rank \(1\).
Complex multiplication
The elliptic curves in class 46800.dc do not have complex multiplication.Modular form 46800.2.a.dc
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
