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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 50715.q
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 50715.q1 | 50715s4 | \([1, -1, 1, -1893443, 1003301142]\) | \(8753151307882969/65205\) | \(5592379919805\) | \([2]\) | \(540672\) | \(2.0406\) | |
| 50715.q2 | 50715s2 | \([1, -1, 1, -118418, 15677232]\) | \(2141202151369/5832225\) | \(500207315049225\) | \([2, 2]\) | \(270336\) | \(1.6940\) | |
| 50715.q3 | 50715s3 | \([1, -1, 1, -72113, 28031406]\) | \(-483551781049/3672913125\) | \(-315011511501238125\) | \([2]\) | \(540672\) | \(2.0406\) | |
| 50715.q4 | 50715s1 | \([1, -1, 1, -10373, 32316]\) | \(1439069689/828345\) | \(71043937499745\) | \([2]\) | \(135168\) | \(1.3474\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 50715.q have rank \(1\).
Complex multiplication
The elliptic curves in class 50715.q do not have complex multiplication.Modular form 50715.2.a.q
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.
