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SageMath
E = EllipticCurve("fc1")
E.isogeny_class()
Elliptic curves in class 244800fc
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 244800.fc2 | 244800fc1 | \([0, 0, 0, -3679500, -2715626000]\) | \(1845026709625/793152\) | \(2368339181568000000\) | \([2]\) | \(5308416\) | \(2.4859\) | \(\Gamma_0(N)\)-optimal |
| 244800.fc3 | 244800fc2 | \([0, 0, 0, -3103500, -3594602000]\) | \(-1107111813625/1228691592\) | \(-3668853434646528000000\) | \([2]\) | \(10616832\) | \(2.8324\) | |
| 244800.fc1 | 244800fc3 | \([0, 0, 0, -10807500, 10338982000]\) | \(46753267515625/11591221248\) | \(34611201186988032000000\) | \([2]\) | \(15925248\) | \(3.0352\) | |
| 244800.fc4 | 244800fc4 | \([0, 0, 0, 26056500, 65561254000]\) | \(655215969476375/1001033261568\) | \(-2989069302509862912000000\) | \([2]\) | \(31850496\) | \(3.3817\) |
Rank
sage: E.rank()
The elliptic curves in class 244800fc have rank \(0\).
Complex multiplication
The elliptic curves in class 244800fc do not have complex multiplication.Modular form 244800.2.a.fc
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 Cremona numbering.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
