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SageMath
E = EllipticCurve("x1")
E.isogeny_class()
Elliptic curves in class 377520.x
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 377520.x1 | 377520x4 | \([0, -1, 0, -1197456, -239709600]\) | \(52337949619538/23423590125\) | \(84984460790651136000\) | \([2]\) | \(8847360\) | \(2.5195\) | |
| 377520.x2 | 377520x2 | \([0, -1, 0, -592456, 173142400]\) | \(12677589459076/213890625\) | \(388014376464000000\) | \([2, 2]\) | \(4423680\) | \(2.1729\) | |
| 377520.x3 | 377520x1 | \([0, -1, 0, -590036, 174644736]\) | \(50091484483024/14625\) | \(6632724384000\) | \([2]\) | \(2211840\) | \(1.8264\) | \(\Gamma_0(N)\)-optimal |
| 377520.x4 | 377520x3 | \([0, -1, 0, -26176, 489806176]\) | \(-546718898/28564453125\) | \(-103636318500000000000\) | \([2]\) | \(8847360\) | \(2.5195\) |
Rank
sage: E.rank()
The elliptic curves in class 377520.x have rank \(1\).
Complex multiplication
The elliptic curves in class 377520.x do not have complex multiplication.Modular form 377520.2.a.x
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.
