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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 46200.a
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 46200.a1 | 46200bs4 | \([0, -1, 0, -393008, -94697988]\) | \(419574424137124/10761135\) | \(172178160000000\) | \([2]\) | \(294912\) | \(1.8388\) | |
| 46200.a2 | 46200bs3 | \([0, -1, 0, -108008, 12342012]\) | \(8709145038724/951192165\) | \(15219074640000000\) | \([2]\) | \(294912\) | \(1.8388\) | |
| 46200.a3 | 46200bs2 | \([0, -1, 0, -25508, -1352988]\) | \(458891455696/65367225\) | \(261468900000000\) | \([2, 2]\) | \(147456\) | \(1.4922\) | |
| 46200.a4 | 46200bs1 | \([0, -1, 0, 2617, -115488]\) | \(7925540864/27286875\) | \(-6821718750000\) | \([2]\) | \(73728\) | \(1.1456\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 46200.a have rank \(2\).
Complex multiplication
The elliptic curves in class 46200.a do not have complex multiplication.Modular form 46200.2.a.a
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.
