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SageMath
E = EllipticCurve("eu1")
E.isogeny_class()
Elliptic curves in class 102960.eu
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 102960.eu1 | 102960ev4 | \([0, 0, 0, -120808587, -511086983366]\) | \(65302476285992806722889/83595669300\) | \(249615330999091200\) | \([2]\) | \(9437184\) | \(3.0463\) | |
| 102960.eu2 | 102960ev3 | \([0, 0, 0, -9496587, -3553136966]\) | \(31720417118313330889/16530220800650700\) | \(49358974827210179788800\) | \([4]\) | \(9437184\) | \(3.0463\) | |
| 102960.eu3 | 102960ev2 | \([0, 0, 0, -7552587, -7981180166]\) | \(15955978629870426889/18037858410000\) | \(53860756606525440000\) | \([2, 2]\) | \(4718592\) | \(2.6997\) | |
| 102960.eu4 | 102960ev1 | \([0, 0, 0, -352587, -189340166]\) | \(-1623435815226889/4247100000000\) | \(-12681772646400000000\) | \([2]\) | \(2359296\) | \(2.3532\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 102960.eu have rank \(0\).
Complex multiplication
The elliptic curves in class 102960.eu do not have complex multiplication.Modular form 102960.2.a.eu
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
