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SageMath
E = EllipticCurve("dv1")
E.isogeny_class()
Elliptic curves in class 129360.dv
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 129360.dv1 | 129360fi4 | \([0, -1, 0, -119229560, 500597895792]\) | \(388980071198593573609/486165942108000\) | \(234278653636870520832000\) | \([2]\) | \(17694720\) | \(3.3932\) | |
| 129360.dv2 | 129360fi2 | \([0, -1, 0, -9469560, 3253383792]\) | \(194878967635813609/103306896000000\) | \(49782591518736384000000\) | \([2, 2]\) | \(8847360\) | \(3.0466\) | |
| 129360.dv3 | 129360fi1 | \([0, -1, 0, -5455480, -4864691600]\) | \(37262716093162729/333053952000\) | \(160495470177681408000\) | \([2]\) | \(4423680\) | \(2.7001\) | \(\Gamma_0(N)\)-optimal |
| 129360.dv4 | 129360fi3 | \([0, -1, 0, 36065160, 25401471600]\) | \(10765621376623941911/6809085937500000\) | \(-3281232492384000000000000\) | \([2]\) | \(17694720\) | \(3.3932\) |
Rank
sage: E.rank()
The elliptic curves in class 129360.dv have rank \(1\).
Complex multiplication
The elliptic curves in class 129360.dv do not have complex multiplication.Modular form 129360.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
