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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 10320.m
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
10320.m1 | 10320e3 | \([0, -1, 0, -7960, 11392]\) | \(54477543627364/31494140625\) | \(32250000000000\) | \([4]\) | \(18432\) | \(1.2815\) | |
10320.m2 | 10320e2 | \([0, -1, 0, -5380, -149600]\) | \(67283921459536/260015625\) | \(66564000000\) | \([2, 2]\) | \(9216\) | \(0.93496\) | |
10320.m3 | 10320e1 | \([0, -1, 0, -5375, -149898]\) | \(1073544204384256/16125\) | \(258000\) | \([2]\) | \(4608\) | \(0.58839\) | \(\Gamma_0(N)\)-optimal |
10320.m4 | 10320e4 | \([0, -1, 0, -2880, -291600]\) | \(-2580786074884/34615360125\) | \(-35446128768000\) | \([2]\) | \(18432\) | \(1.2815\) |
Rank
sage: E.rank()
The elliptic curves in class 10320.m have rank \(0\).
Complex multiplication
The elliptic curves in class 10320.m do not have complex multiplication.Modular form 10320.2.a.m
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.