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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 36100.a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
36100.a1 | 36100j3 | \([0, 1, 0, -373033, 87550188]\) | \(488095744/125\) | \(1470183781250000\) | \([2]\) | \(248832\) | \(1.8963\) | |
36100.a2 | 36100j4 | \([0, 1, 0, -327908, 109571188]\) | \(-20720464/15625\) | \(-2940367562500000000\) | \([2]\) | \(497664\) | \(2.2429\) | |
36100.a3 | 36100j1 | \([0, 1, 0, -12033, -353312]\) | \(16384/5\) | \(58807351250000\) | \([2]\) | \(82944\) | \(1.3470\) | \(\Gamma_0(N)\)-optimal |
36100.a4 | 36100j2 | \([0, 1, 0, 33092, -2338812]\) | \(21296/25\) | \(-4704588100000000\) | \([2]\) | \(165888\) | \(1.6936\) |
Rank
sage: E.rank()
The elliptic curves in class 36100.a have rank \(1\).
Complex multiplication
The elliptic curves in class 36100.a do not have complex multiplication.Modular form 36100.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.