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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 23100c
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 23100.d1 | 23100c1 | \([0, -1, 0, -56133, 10609137]\) | \(-4890195460096/9282994875\) | \(-37131979500000000\) | \([]\) | \(186624\) | \(1.8692\) | \(\Gamma_0(N)\)-optimal |
| 23100.d2 | 23100c2 | \([0, -1, 0, 483867, -224560863]\) | \(3132137615458304/7250937873795\) | \(-29003751495180000000\) | \([]\) | \(559872\) | \(2.4185\) |
Rank
sage: E.rank()
The elliptic curves in class 23100c have rank \(0\).
Complex multiplication
The elliptic curves in class 23100c do not have complex multiplication.Modular form 23100.2.a.c
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
