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SageMath
E = EllipticCurve("eu1")
E.isogeny_class()
Elliptic curves in class 304920.eu
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 304920.eu1 | 304920eu3 | \([0, 0, 0, -32426427, 71060048246]\) | \(1425631925916578/270703125\) | \(715989842013600000000\) | \([2]\) | \(15728640\) | \(3.0028\) | |
| 304920.eu2 | 304920eu4 | \([0, 0, 0, -14218347, -19982843386]\) | \(120186986927618/4332064275\) | \(11457991169662376908800\) | \([2]\) | \(15728640\) | \(3.0028\) | |
| 304920.eu3 | 304920eu2 | \([0, 0, 0, -2239347, 863012414]\) | \(939083699236/300155625\) | \(396944768412339840000\) | \([2, 2]\) | \(7864320\) | \(2.6562\) | |
| 304920.eu4 | 304920eu1 | \([0, 0, 0, 396033, 91900226]\) | \(20777545136/23059575\) | \(-7623859837760812800\) | \([2]\) | \(3932160\) | \(2.3097\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 304920.eu have rank \(0\).
Complex multiplication
The elliptic curves in class 304920.eu do not have complex multiplication.Modular form 304920.2.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.
