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SageMath
E = EllipticCurve("dv1")
E.isogeny_class()
Elliptic curves in class 425880.dv
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
425880.dv1 | 425880dv5 | \([0, 0, 0, -37112907, 87002074406]\) | \(784478485879202/221484375\) | \(1596102169989600000000\) | \([2]\) | \(37748736\) | \(3.0495\) | \(\Gamma_0(N)\)-optimal* |
425880.dv2 | 425880dv3 | \([0, 0, 0, -2616627, 989049854]\) | \(549871953124/200930625\) | \(723991944307282560000\) | \([2, 2]\) | \(18874368\) | \(2.7030\) | \(\Gamma_0(N)\)-optimal* |
425880.dv3 | 425880dv2 | \([0, 0, 0, -1126047, -448763614]\) | \(175293437776/4862025\) | \(4379704354451462400\) | \([2, 2]\) | \(9437184\) | \(2.3564\) | \(\Gamma_0(N)\)-optimal* |
425880.dv4 | 425880dv1 | \([0, 0, 0, -1118442, -455268931]\) | \(2748251600896/2205\) | \(124141279888080\) | \([2]\) | \(4718592\) | \(2.0098\) | \(\Gamma_0(N)\)-optimal* |
425880.dv5 | 425880dv4 | \([0, 0, 0, 242853, -1470236794]\) | \(439608956/259416045\) | \(-934726236003374330880\) | \([2]\) | \(18874368\) | \(2.7030\) | |
425880.dv6 | 425880dv6 | \([0, 0, 0, 8030373, 6996087254]\) | \(7947184069438/7533176175\) | \(-54286984532572352870400\) | \([2]\) | \(37748736\) | \(3.0495\) |
Rank
sage: E.rank()
The elliptic curves in class 425880.dv have rank \(0\).
Complex multiplication
The elliptic curves in class 425880.dv do not have complex multiplication.Modular form 425880.2.a.dv
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.
\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 8 & 8 & 4 \\ 2 & 1 & 2 & 4 & 4 & 2 \\ 4 & 2 & 1 & 2 & 2 & 4 \\ 8 & 4 & 2 & 1 & 4 & 8 \\ 8 & 4 & 2 & 4 & 1 & 8 \\ 4 & 2 & 4 & 8 & 8 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.