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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 21675.m
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 21675.m1 | 21675p2 | \([0, 1, 1, -428683, -108234581]\) | \(-23100424192/14739\) | \(-5558806710796875\) | \([]\) | \(186624\) | \(1.9621\) | |
| 21675.m2 | 21675p1 | \([0, 1, 1, 4817, -618206]\) | \(32768/459\) | \(-173111627671875\) | \([]\) | \(62208\) | \(1.4128\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 21675.m have rank \(0\).
Complex multiplication
The elliptic curves in class 21675.m do not have complex multiplication.Modular form 21675.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
