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SageMath
E = EllipticCurve("ev1")
E.isogeny_class()
Elliptic curves in class 14400.ev
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 14400.ev1 | 14400ee3 | \([0, 0, 0, -194700, -33046000]\) | \(546718898/405\) | \(604661760000000\) | \([2]\) | \(98304\) | \(1.7700\) | |
| 14400.ev2 | 14400ee4 | \([0, 0, 0, -122700, 16346000]\) | \(136835858/1875\) | \(2799360000000000\) | \([2]\) | \(98304\) | \(1.7700\) | |
| 14400.ev3 | 14400ee2 | \([0, 0, 0, -14700, -286000]\) | \(470596/225\) | \(167961600000000\) | \([2, 2]\) | \(49152\) | \(1.4234\) | |
| 14400.ev4 | 14400ee1 | \([0, 0, 0, 3300, -34000]\) | \(21296/15\) | \(-2799360000000\) | \([2]\) | \(24576\) | \(1.0769\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 14400.ev have rank \(1\).
Complex multiplication
The elliptic curves in class 14400.ev do not have complex multiplication.Modular form 14400.2.a.ev
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.
