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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 18480a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
18480.c3 | 18480a1 | \([0, -1, 0, -511, 4606]\) | \(924093773824/3565485\) | \(57047760\) | \([2]\) | \(6144\) | \(0.34653\) | \(\Gamma_0(N)\)-optimal |
18480.c2 | 18480a2 | \([0, -1, 0, -756, 0]\) | \(186906097744/108056025\) | \(27662342400\) | \([2, 2]\) | \(12288\) | \(0.69310\) | |
18480.c1 | 18480a3 | \([0, -1, 0, -8456, -295680]\) | \(65308549273636/204604785\) | \(209515299840\) | \([2]\) | \(24576\) | \(1.0397\) | |
18480.c4 | 18480a4 | \([0, -1, 0, 3024, -3024]\) | \(2985557859644/1729468125\) | \(-1770975360000\) | \([2]\) | \(24576\) | \(1.0397\) |
Rank
sage: E.rank()
The elliptic curves in class 18480a have rank \(1\).
Complex multiplication
The elliptic curves in class 18480a do not have complex multiplication.Modular form 18480.2.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 Cremona numbering.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.